Apparatus for Folding a Sheet of Material Into a Support Structure

ABSTRACT

Apparatus and methods for forming three dimensional structures from a sheet of material of a desired medium are described. Examples described include an apparatus for folding a sheet of material to create a folded structure, the apparatus having a first and second array of creasing elements, and at least one actuator for causing relative movement of the first and second array of creasing elements from a first position to a second position.

TECHNICAL FIELD

This present disclosure relates to apparatus for folding a sheet ofmaterial, and more particularly apparatus for folding a sheet ofmaterial into a three dimensional structure.

BACKGROUND

Sandwiched structures are known in the art. Some sandwich structures areformed using corrugated materials, which may be fluted by passing amaterial between rollers. Other sandwiched structures may be formedusing core materials, for example honeycomb cores or foam cores, whichmay be sandwiched or disposed between one or more ply sheets or externalliners.

However, conventional sandwich structures exhibit many drawback instrength, rigidity, weight, and durability. Improved three dimensionalsupport structures have been introduced, as described in U.S. Pat. No.7,762,932, which is incorporated herein in its entirety by thisreference for any purpose. Instead of corrugating the core or innermedium of the structure, the three dimensional support structuresdescribed in U.S. Pat. No. 7,762,932 are generally formed by folding asheet of medium, which may be paper or other foldable medium, into athree dimensional structure.

While certain processes for large scale production of corrugatedstructures may be known, methods and apparatus for obtaining foldedthree dimensional structures in an automated fashion are not currentlyavailable. The present disclosure may address some or all of theshortcomings in the art.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other features of the present disclosure will becomemore fully apparent from the following description and appended claims,taken in conjunction with the accompanying drawings. Understanding thatthese drawings depict only several examples in accordance with thedisclosure and are, therefore, not to be considered limiting of itsscope, the disclosure will be described with additional specificity anddetail through use of the accompanying drawings, in which:

FIG. 1 is an isometric and schematic view of an apparatus of the presentinvention for folding a sheet of material into a support structure.

FIG. 2 is a front elevational view of the apparatus of FIG. 1 takenalong the line 2-2 of FIG. 1.

FIG. 3 is a side elevational view of the apparatus of FIG. 1 taken alongthe line 3-3 of FIG. 2.

FIG. 4 is an isometric view of the bottom half of the apparatus of FIG.1 in the fully-disengaged position.

FIG. 5 is a plan view of an unfolded sheet of material for use informing the support structure.

FIG. 6 is a perspective view of the sheet of material of FIG. 5partially folded into the support structure.

FIG. 7 is a perspective view of the sheet of material of FIG. 5 fullyfolded into the support structure.

FIG. 8 is a perspective view of the support structure of FIG. 7 takenalong the line 8-8 of FIG. 7.

FIG. 9 is a perspective view of a portion of the sheet of material ofFIG. 5 as partially folded in FIG. 6.

FIG. 10 is a perspective view of the portion of the sheet of material ofFIG. 5 fully folded to form a portion of the support structure of FIG.7.

FIG. 11 is a front elevational view of the bottom half of the apparatusof FIG. 4 taken along the line 11-11 of FIG. 4.

FIG. 12 is a top plan view of the bottom half of the apparatus of FIG. 4taken along the line 12-12 of FIG. 11.

FIG. 13 is a side elevational view of the bottom half of the apparatusof FIG. 4 taken along the line 13-13 of FIG. 12.

FIG. 14 is a side-perspective isometric view of a portion of an array ofcreasing elements of the bottom half of the apparatus of FIG. 4.

FIG. 15 is a top plan view of the portion of the array of creasingelements of FIG. 14 taken along the line 15-15 of FIG. 14.

FIG. 16 is a side-perspective isometric view of portions of the firstand second arrays of creasing elements of the apparatus of FIG. 1 in anopposed first position.

FIG. 17 is a side-perspective isometric view, similar to FIG. 16, ofportions of the first and second arrays of creasing elements of FIG. 16in an opposed position with an unfolded sheet of material disposedtherebetween.

FIG. 18 is a somewhat schematic, isometric view of the unfolded sheet ofmaterial of FIG. 5.

FIG. 19 is a front elevational view of the portion of the first andsecond arrays of creasing elements of FIG. 16 taken along the line 19-19of FIG. 17.

FIG. 20 is a side elevational view of the portion of the first andsecond arrays of creasing elements of FIG. 16 taken along the line 20-20of FIG. 19.

FIG. 21 is a side-perspective isometric view of the portion of the firstand second arrays of creasing elements of FIG. 16 in a partially engagedposition with a partially folded sheet of material disposedtherebetween.

FIG. 22 is a somewhat schematic, isometric view of the partially foldedsheet of material of FIG. 6.

FIG. 23 is a front elevational view of the portion of the first andsecond arrays of creasing elements of FIG. 21 taken along the line 23-23of FIG. 21.

FIG. 24 is a side elevational view of the portion of the first andsecond arrays of creasing elements of FIG. 21 taken along the line 24-24of FIG. 23.

FIG. 25 is an isometric view of the bottom half of the apparatus of FIG.1 in a fully-engaged position.

FIG. 26 is a front elevational view of the bottom half of the apparatusof FIG. 25 taken along the line 26-26 of FIG. 25.

FIG. 27 is a side elevational view of the bottom half of the apparatusof FIG. 25 taken along the line 27-27 of FIG. 26.

FIG. 28 is a side-perspective isometric view of the portion of the firstand second arrays of creasing elements of FIG. 16 in a fully engagedposition with a fully folded sheet of material disposed therebetween.

FIG. 29 is a front elevational view of the portion of the first andsecond arrays of creasing elements of FIG. 28 taken along the line 29-29of FIG. 28.

FIG. 30 is a side elevational view of the portion of the first andsecond arrays of creasing elements of FIG. 28 taken along the line 30-30of FIG. 28.

FIG. 31 is a somewhat schematic, isometric view of a portion of thefully folded sheet of material of FIG. 7.

FIG. 32 is an isometric and schematic partial view of another embodimentof an apparatus of the present invention for folding a sheet of materialinto a support structure.

FIG. 33 is a side elevational view, similar to FIG. 20, of a portion ofthe first and second arrays of creasing elements of the apparatus ofFIG. 32.

FIG. 34 is a side-perspective isometric view, similar to FIG. 14, ofanother embodiment of a portion of an array of creasing elements of thepresent invention.

FIG. 35 is a front perspective isometric view of the portion of thearray of creasing elements of FIG. 34 taken along the line 35-35 of FIG.34.

FIG. 36 is a front elevational view of the portion of the array ofcreasing elements of FIG. 34 taken along the line 36-36 of FIG. 34.

DETAILED DESCRIPTION

In the following detailed description, reference is made to theaccompanying drawings, which form a part hereof. In the drawings,similar symbols typically identify similar components, unless contextdictates otherwise. The illustrative examples described in the detaileddescription, drawings, and claims are not meant to be limiting. Otherexamples may be utilized, and other changes may be made, withoutdeparting from the spirit or scope of the subject matter presentedherein. It will be readily understood that the aspects of the presentdisclosure, as generally described herein, and illustrated in theFigures, can be arranged, substituted, combined, separated, and designedin a wide variety of different configurations, all of which areimplicitly contemplated herein.

Apparatus, systems and methods for folding a sheet of material into afolded support structure are described herein, which apparatus, systems,and methods, as will be appreciated, lend themselves to a level ofautomation. An exemplary apparatus includes a first array of creasingelements and a second array of creasing elements, each of the creasingelements in the first and second arrays having a leading edge adapted toengage a sheet of material. The apparatus further includes at least onefirst actuator for causing relative movement of the first and secondarrays of creasing elements from a first position in which the first andsecond plurality of creasing elements are spaced apart to a secondposition in which the first and second array of creasing elements are atleast partially interdigitated whereby the sheet of material can beplaced between the first and second arrays of creasing elements andfolded by the leading edges of the creasing elements during the relativemovement of the first and second arrays creasing elements to the secondposition. The apparatus also includes at least one second actuator formoving the creasing elements of the first array closer together and thecreasing elements of the second array closer together during relativemovement of the first and second arrays of creasing elements to thesecond position whereby the movement of the creasing elements of thefirst array closer together and the creasing elements of the secondarray closer together accommodates contraction of the sheet of materialas it is folded by the first and second arrays of creasing elements.

An exemplary apparatus for folding a sheet of material into a supportstructure according to the present invention is illustrated in FIGS.1-4. Exemplary folding apparatus 1 therein may include a supportstructure 3, an actuation assembly 5 including a plurality of actuators,and a creasing assembly 7 including a first or top array 10 of creasingelements and a second or bottom array 12 of creasing elements. Thesupport structure 3 generally includes any structural features providedfor supporting and maintaining the relative positioning betweencomponents of the actuation assembly 5 and creasing assemblies 7. Theactuation assembly 5 can include an suitable actuation device such as apump, motor or other mechanical or electrical actuator adapted forgenerating and providing the desired movement of the components of thecreasing assembly 7, for example the movement of creasing arrays 10, 12and creasing elements relative to each other. In the context of thisdisclosure, creasing elements may interchangeably be referred to asfolding elements and accordingly, the term “folding element” is analternate term for “creasing element.” The creasing assembly 7 includesstructures configured to engage with a folding medium to obtain a foldedthree dimensional structure as will be described.

In the creasing assembly 7, a first array 10 of creasing elements and asecond array 12 of creasing element including a respective plurality ofindividual top creasing elements 13 and bottom creasing elements 14 canbe provided, each creasing element 13, 14 being configured to engagewith a foldable medium during operation of the apparatus 1 to fold themedium according to a desired pattern. In the exemplary apparatus 1, thecreasing assembly 7 has a first or top array 10 of creasing elements 13and a second or bottom array 12 of creasing elements 14, each asdescribed in further detail below. As will be understood, designationsof relative positioning such as “top,” “bottom,” “left,” “right,” andsimilar identifiers are used herein only for the purposes offacilitating the description of the examples disclosed herein and arenot to be taken in a limiting sense.

The support structure 3 may include a plurality of support elements ormembers, which can include platforms or plates, which may be generallyrigid and used to mount various components of the actuation assembly 5and creasing assembly 7 thereto. A first or top support member or plate2 and a second or bottom support member or plate 4 may remain stationaryrelative to each other during the operation of the device, andaccordingly may be respectively referred to herein as stationary topplatform 2 and a stationary base platform 4. A third or intermediatesupport member or plate 6 may be provided between the top plate 2 andbottom plate 4. The third or intermediate plate 6 may be configured tomove relative to the first and/or second plates 2, 4 during operation ofthe folding apparatus 1. In one embodiment, illustrated in FIG. 1, firstplate 2, second plate 4, and intermediate plate 6 are each generallyrectangular in shape and each extend in the x-y plane, noted in FIG. 1,and are disposed in spaced-apart positions along the z axis andgenerally parallel to each other. In one embodiment, intermediate ormoveable plate 6 is movable along the z axis or vertical direction 15relative to and between both top plate 2 and bottom plate 4. Each of theplates 2, 4, 6 may be made from any suitable rigid material such asmetal, plastic or ceramic. It is appreciated that other form factors andrelative arrangement may be used in other embodiments of the invention.

The support structure 3 may also include one or more support members 9.The support members may be implemented as posts or columns 11 extendingbetween the top plate 2 and the bottom plate 4. The guide columns 11 aremounted or secured to and support the top plate 4 in a fixed positionrelative to the bottom plate 2. Each of the columns has a first or topend secured to top plate 2 and a second or bottom end secured to bottomplate 4. The columns 11 may, in some examples, be used as verticalmovement guides for the vertical movement of the intermediate plate 6relative to and between the plates 2, 4. In one embodiment, four supportmembers or columns 11 are provided, one at each corner of plates 2, 4and as shown in FIGS. 1-3, however it is appreciated that any number ofsupport members 11 may be used as desired or suitable for the particularapplication. In some examples the plates or platforms 2, 4, 6 may becircular, for example, and different number of columns, for examplethree in number, or in some examples six or eight columns may be used tomaintain the plates in the desired configuration. It is appreciated thatother mechanisms, structures, guides or elements may be provided forpermitting intermediate plate 6 to move relative to top and bottomplates 2, 4 and for guiding the intermediate plate 6 during suchmovement.

The intermediate plate 6, which is provided between the first plate 2and second plate 4, is configured to move in the vertical direction 15,for example the direction perpendicular to the respective planes of topand bottom plates 2, 4 and thus along the z axis or vertical direction15, during the operation of exemplary apparatus 1. A plurality ofapertures or openings may be provided through the thickness of theintermediate plate 6 such that the columns 11 can pass through the plate6 and the plate 6 can move up and down, using the columns 11 as guides.Each of the apertures may include a bearing assembly or any otherconventional sliding contact mechanism (not shown) for slidinglycoupling the support member within the aperture to the intermediateplate 6. The bearing may be selected such that it provides a nominallyfrictionless contact between surfaces of the columns 11 and theapertures. In some examples, one or more surfaces of the aperturesand/or columns may be treated or otherwise coated with a low-frictioncoating to reduce friction between and minimize wear of the surfaces ofthe columns 11 and apertures as the plate 6 moves up and down. In oneembodiment, some or all of the columns 11 are cylindrical and theapertures in plate 6 are circular, although it is appreciated that othercooperatively engaging cross-sectional configurations, such as oval,rectangular or square, can be provided.

In one embodiment, a plurality of linear actuators, for examplecylinder-piston type, hydraulic or electric actuators, may be usedinstead of the stationary support members or columns 11. That is, insome examples, a first plurality of pistons or actuators (not shown) maybe provided between the first plate 2 and the intermediate plate 6 and asecond plurality of pistons (non shown) may be provided between theintermediate plate 6 and the second plate 4. The movement of the linearactuators may be controlled and/or synchronized as desired, using aprogrammable controller for example, to provide coordinated movement ofsuch actuators and thus corresponding movement of the intermediate plate6 along the z axis or vertical direction 15.

Actuation assembly 5 may generally include actuation devices for causingrelative movement between the first array 10 and the second array 12between a first or home position where the first array 10 and secondarray 12 are spaced apart, as shown for example in FIGS. 2, 3, 16, 17,19 and 20, and a second position where the creasing elements of thefirst array 10 and second array 12 are interdigitated, as shown forexample in FIGS. 21, 23 and 24. In the example in FIGS. 1-3, by virtueof the arrays 10, 12 being mounted to two separate respective plates orplatforms, movement of the arrays 10, 12 towards or away from each otheris achieved by one or more actuators configured to move one or both ofsuch plates towards or away from each other. In one embodiment, firstarray 10 is mounted on the intermediate plate 6, for example on thelower or inner-facing surface of the intermediate plate 6, and secondarray 12 is mounted on bottom plate 4, for example on the upper orinner-facing surface of the bottom plate 4 and thus arrays 10, 12 faceor are opposed to each other. The actuators of actuation assembly 5 canserve to cause intermediate plate 6 to move downwardly or towards bottomplate 4, or cause bottom plate 4 to move upwardly or towardsintermediate plate 6, or both. In one embodiment the actuation assembly5 moves intermediate plate 6 downwardly relative to bottom plate 4, andtop plate 2, and the bottom and top plates 4, 2 remain stationary, andin this manner first or top array 10 is moved from a first or homeposition in which the creasing elements 13 of the top array are spacedfrom the creasing elements 14 of the bottom array 12 to a secondposition in which the creasing elements 13 of the top array 10 are atleast partially interdigitated with the creasing elements 14 of thebottom array 12. The actuation assembly 5 may also include actuationdevices configured to move the creasing element 13, 14 and/or arrays 10,12 in the x-y plane, for example longitudinally and laterally.

An exemplary operation of the apparatus will be briefly described tofurther aid in understanding the components and functions of theactuation assembly. Generally, during operation, the first array 10 andsecond array 12 and respective individual creasing elements or foldingelements 13, 14 of the arrays are configured to move along the x and ydirections. At some stages of a folding operation the individualcreasing elements, for example creasing elements or folding elements 13and 14, of the first array 10 and the second array 12 move between afirst or fully expanded position, as illustrated in FIG. 4, and a secondor fully contracted position, as illustrated in FIG. 25. In the fullyexpanded or home position, the creasing elements 13, 14 are spacedfarther apart from each other more than when the creasing elements arein the fully contracted position, in which the creasing elements arecloser together. In one embodiment, for example as shown in FIGS. 25-30,adjacent creasing elements are at least nearly touching each other andcan in fact touch each other when the respective array is in the fullycontracted position. Accordingly in some instances, the first or toparray 10 and/or the second or bottom array 12 may be said to be in anexpanded configuration, for example when the creasing elements arespaced apart, or in a collapsed configuration, for example when thecreasing elements are close together. The arrays 10 and 12 can passthrough several intermediate stages of being partially expanded orcollapsed along the x and y directions when moving between such firstand second positions. Contraction and expansion of the creasing elementsof an array 10, 12 in the x direction can be coordinated with orindependent of the contraction and expansion of such creasing elementsin the y direction. In addition, contraction and expansion of creasingelements 13 in one array 10 and can be coordinated with or independentof the contraction and expansion of creasing elements 14 in the otherarray 12.

In addition, the first or top array 10 is also configured to translateor move up and down, that is along the z axis and vertical direction 15,relative to the second or bottom array 12 (see FIGS. 1-3). At somestages of a folding operation the individual creasing elements, forexample creasing elements 13 and 14, of the first array 10 and thesecond array 12 move relative to each other between a first orspaced-apart or non-interdigitated position, as illustrated in FIGS.1-3, 16-17, and a second or fully interdigitated position, asillustrated in FIGS. 28-30. In the first expanded position, the creasingelements 13, 14 are spaced farther apart from each other and the leadingedges 120 of the creasing elements 13 are not interdigitated with theleading edges 122 of the creasing elements 14. In one embodiment, forexample as shown in FIGS. 28-30, the top portion 150 of the creasingelements 13 are fully interdigitated with the top portion 150 ofcreasing elements 14 when the arrays 10, 12 are fully interdigitatedrelative to or with each other. In one embodiment, the inclined surfaces124, 126 of creasings elements 13 are in contact with or in closedproximity to and substantially parallel to the opposed inclined surfaces124, 126 of the creasing elements 14 when the arrays 10, 12 are fullyinterdigitated relative to each other. The arrays 10 and 12 can passthrough several intermediate stages of being partially interdigitated inz direction when moving between such first and second positions.Interdigitation of the arrays 10, 12 in the z direction can becoordinated with or independent of the contraction and expansion one orboth of the arrays in the x direction and in the y direction. Forexample, the relative movement of the arrays 10, 12 can be coordinatedsuch that the arrays are fully contracted in the x and y directions andwhen the arrays are fully interdigitated in the z direction. It isappreciated that many combinations of independent or coordinatedmovement of the creasing elements or folding elements of one array inthe x, y and z directions, or of the creasing elements or foldingelements of both arrays in the x, y and z directions, can be provided byapparatus 1.

Movement of the arrays 10, 12 and creasing elements 13, 14 along the xand/or y direction is provided by one or more array actuation assembliesor devices 22. Movement in the vertical direction 15 of one or more ofthe arrays is provided using one or more plate actuation assemblies ordevices 25. This combination of array and plate actuation devices oractuators is configured to provide three-degrees of freedom of thecreasing elements 13, 14 of each of the arrays 10, 12, for examplemovement along all three of the x, y and z axes, such that each creasingelement in an array 10 or 12 is moveable along the x, y, and z axesrelative to the creasing elements in the other array 12 or 10. Hence,for example, each creasing element 13 in the top array 10 is movablealong all three orthogonal x, y and z axes relative to the creasingelements 14 in the bottom array 12. In one embodiment, creasing elements13, 14 are restrained from rotational movement along all of the axes,however it is appreciated that arrays of creasing elements may beprovided that rotate or pivot along one or any combination of axes suchthat various curved structures may be manipulated or formed using theapparatus described herein.

Generally, the arrays 10, 12 and individual creasing elements 13, 14 areconfigured for linear motion along the x, y and z axes according to adesired timing or sequence to achieve the folding of a sheet of materialinto a folded support structure, as will be described herein. The timingand sequence of relative motion of the arrays and creasing elements maybe controlled with one or more manual or programmable controllers (notshown), which are operatively coupled for example by hard wiring orwireless communication to the actuation assembly 5.

In one embodiment, plate actuation may be accomplished by a plateactuation assembly or device 25 that includes one or more linearactuators 8, for example piston-type actuator that can be hydraulic,pneumatic or electric or any other linear actuators currently known orlater developed. In the present example, a single actuator 8 having ahousing 8 a and a piston 8 b that is extendable from the housing 8 a ina linear manner is used, with the first or free end of the piston 8 bsecured to the intermediate or moveable plate 6 and the housing 8 abeing secured to the top plate 2. In this manner, as the first end ofthe piston 8 b moves away from or extends from the actuator housing 8 a,plate 6 is translated or moved downwardly on columns 11 along the zdirection to a position closer to the bottom plate 4, thus contractingthe creasing assembly 7 in the z direction by causing the creasingelements 13 of the top array 10 to interdigitate with the creasingelements 14 of the bottom array 12. When the piston 8 b retracts intothe housing 8 a, moveable plate 6 is translated or moved upwardly andaway from the bottom plate 4, thus expanding the creasing assembly 7along the z direction by causing the creasing elements 13 of the toparray 10 to move away from the creasing elements 14 of the bottom array12.

As will be appreciated, in some examples, any number of actuators 8 maybe used in plate actuation device or assembly 25. For example, in otherembodiments, two or more actuators 8, and in some embodiments smalleractuators 8, may be used in place of a single central actuator 8. Inother examples, four actuators 8 may be used, which may for example belocated at each corner of the apparatus 1, such as at each corner of topplate 2 and intermediate plate 6. As previously described, in someexamples, the linear actuation of the plate 6 may be achieved byreplacing the support members or columns 11 with active components, forexample linear actuators. In one embodiment (not shown), a rack andpinion gearing mechanism may be used to provide linear actuation of theintermediate plate 6. Any other actuation devices 8 currently known orlater developed may be used to move the plate 6 and thus move the arrays10, 12 closer together and farther apart, that is provide verticalmovement of one or both of the arrays 10, 12.

The actuation assembly 5 may also include an array actuation assembly ordevice 22 for providing movement of the first array 10 and second array12 of creasing elements 13, 14 and the individual creasing elements 13,14 along the x and/or y directions, for example lateral and/orlongitudinal movement in the x-y plane. Array actuation assembly 22 maybe implemented using any combination of hydraulic, pneumatic orelectrical actuators, piston-type or otherwise. In some examples, thearray actuation assembly 22 may include one or more hydraulically orpneumatically-driven rotary actuators. In some examples, electricalmotors or other electrical actuators may be used to provide the desiredmovement of the arrays 10, 12 and associated creasing elements 13, 14 inthe x-y plane. The x-y plane, as used in the context of the presentdisclosure, is meant to refer to some reference x-y plane, for examplethe x-y plane illustrated in FIG. 1, as well as any plane parallel tosuch reference x-y plane.

In one embodiment of apparatus 1, array actuation assembly 22 forcausing longitudinal and lateral actuation of the arrays 10, 12 ofcreasing elements includes a plurality of rotary actuators, such asfirst or top rotary actuators 18 and second or bottom actuators 20. Thearray actuation assembly may, in addition, include a plurality motionconverters or transmission mechanisms, such as first or top gearmechanisms 42 and second or bottom gear mechanism 45, for converting therotation of the shafts of the respective actuators 18, 20 to linearmotion. The gear mechanisms 42, 45 may be of the rack and pinion type,and in one embodiment may include a central gear or pinion and a pair oflinear bar gears or racks, each of the pair of racks being disposed onopposite sides of the pinion gear and engaged with the teeth of thepinion gear. The components of each of gear mechanisms 42, 45 may bemade from any suitable material such as metal or plastic. In oneembodiment of apparatus 1, four rotary top actuators 18 are mounted tothe intermediate plate 6 and move up and down with the plate 6 and fourrotary bottom actuators 20 are mounted on the bottom plate 2, and remainstationary with such plate 2. Each of the plurality of actuators 18 and20 is configured to rotate a one of the circular gears or pinions of therespective rack and pinion assemblies 42 and 45 to cause the related bargear or rack of the respective rack and pinion assembly 42 and 45 totranslate along the x or y directions. In some embodiments, certaincoupling devices may be used, if desired, to couple the rotation of asingle actuator to a plurality of rack and pinion assemblies, such thatfewer number of actuators may be needed.

FIGS. 4, and 11-13 show perspective, side, and top views of the bottomhalf 1 a of the folding apparatus 1, and specifically bottom plate 4,bottom actuators 20, bottom rack and pinion assemblies 45 and bottomarray 12 mounted on the bottom plate 4 and more particularly carried bythe bottom rack and pinion assemblies 45. The bottom half assembly 1 aincludes four rotary actuators 20 as described above and four sets ofrack and pinion gears 45 a, 45 b, 45 c and 45 d, described in furtherdetail below. A first bottom rack and pinion gear assembly 45 a, whichis arranged along the x axis and adapted for x movement, includes afirst x-pinion 17 and a first pair of x-racks including inner bar gearor rack 19 and outer bar gear or rack 21. The first pair of x-racks areprovided on a first pair of x-rails. That is, the inner rack 19 isslidably coupled to inner rail 23 and outer rack 21 is slidably coupledto outer rail 24 in each case for example by a set of bearing mechanismsor bearings 40. Any bearing mechanism currently known or later developedmay be used to slidably couple the inner and outer racks 17, 19 to therespective inner and outer rails 23, 24. The x-rails 23 and 24 may berigidly mounted by any suitable means, for example by being bolted,welded or otherwise affixed, to bottom plate or platform 2. The firstx-pinion 17 is coupled to and rotated by a first rotary actuator 20 aduring operation of the array actuation assembly or device 22, saidrotation being transmitted to the racks 19, 21 which are configured toslide along the x-rails in the x direction, as shown for example bycomparison of FIG. 4 and FIG. 25. During such movement or translation,the outer gear teeth on pinion 17 are rotated by actuator 20 a and meshwith the respective teeth of racks 19, 24 to cause the racks to slide ormove in opposite linear directions on the respective rails 23, 24,either towards each other in a contraction motion of the assembly 45 aor away from each other in an extension motion of the assembly 45 a.

A second bottom rack and pinion gear assembly 45 c is also arrangedalong the x axis and adapted for x movement. The second rack and piniongear assembly 45 c is disposed generally opposite the first bottom rackand pinion gear assembly 45 a, that is on the opposing side of thebottom array 12 of creasing elements 13. The second gear assembly 45 cis substantially similar in construction and operation to first gearassembly 45 a and includes a second x-pinion 37 and a second pair ofx-racks including second inner bar gear or rack 39 and second outer bargear or rack 41. The second pair of x-racks are provided on a secondpair of x-rails, the rails being mounted to plate 2. That is, the secondinner rack 39 is slidable coupled to second inner rail 43 and secondouter rack 41 is coupled to second outer rail 44 by any suitable meanssuch as by respective sets of bearings 40. The second x-pinion 37 iscoupled to and rotated by a rotary actuator 20 c during operation of thedevice, and rotation of the pinion 37 is used to translate the racks 39and 41 in x direction in the manner discussed above with respect tofirst bottom rack and pinion gear assembly 45 c.

Two additional rack and pinion gear assemblies 45 b, 45 d, eachsubstantially similar to assemblies 45 a and 45 c, may be provided alongthe y direction and adapted for y movement in a direction perpendicularto the movement of assemblies 45 a and 45 c. A third rack and piniongear assembly 45 b includes a third pinion gear or first y-pinion gear27 and a third pair of racks also known as first pair of y-racks,including third inner bar gear or rack 28 and third outer bar gear orrack 26. Similar to the gear assembly 45 a, the racks 28 and 26 areslidably coupled or engaged with a third pair of rails also referred toas a first pair of y-rails, such as third inner rail 29 and third outerrail 30, by any suitable means such as a by respective sets of bearings40, and the racks 28 and 26 are configured to traverse along the ydirection in response to the rotation of third actuator 80 b that isconnected to third pinion gear 27 in the manner discussed above withrespect to first bottom rack and pinion gear assembly 45 d. Similarly, afourth rack and pinion assembly 45 d is provided on the opposite side ofthe bottom array 12 of creasing elements 14 from the third rack andpinion gear assembly 45 b. Fourth rack and pinion gear assembly 45 dincludes a fourth pinion gear or first y-pinion gear 47 and a fourthpair of racks also known as second pair of y-racks, including fourthinner bar gear or rack 48 and fourth outer bar gear or rack 46. Similarto the third gear assembly 45 b, the racks 48 and 46 are slidablycoupled or engaged with a fourth pair of rails also referred to as asecond pair of y-rails, such as fourth inner rail 49 and fourth outerrail 50, by any suitable means such as a by respective sets of bearings40, and the racks 48 and 46 are configured to traverse along the ydirection in response to the rotation of fourth actuator 80 d that isconnected to third pinion gear 47 in the manner discussed above withrespect to first bottom rack and pinion gear assembly 45 d.

The actuation assembly 22 may further include a plurality of x-push/pullor translation bars 51, 52 and y-push/pull or translation bars 53, 54,operatively coupled to the bottom array 12 and configured to collapsethe array 12. In one embodiment, each of the push/pull or translationbars 51-54 may be a generally elongate members which is coupled at itsopposite ends to opposite respective rack gears, such as opposite setsof the racks discussed above. The push/pull bars may also be coupled tothe sides of the bottom array 12, or may be otherwise configured toapply a generally inward force to cause the bottom array 12, under theforce of the rack and pinion assemblies discussed above, to contract orcollapse. The push/pull bars also apply a generally outward force tocause the bottom array 12, under the force of the rack and pinionassemblies discussed above, to expand.

In one embodiment, as shown in FIG. 12, a first x-push/pull bar 51 isdisposed such that a longitudinal direction of the push/pull bar 51extends in the y direction. The push/pull bar 51 is attached at a firstend to the top of one end of the outer rack 21 of the first rack andpinion assembly 45 a and is attached at its opposite second end to thetop of an end of the inner rack 39 of the second rack and pinionassembly 45 c, in each case by any suitable means such as an adhesive orone or more fasteners. The central portion of the bar 51 abuts a side,such as the left side in FIG. 12, of the bottom array 12 and is attachedto such side of array 12 by at least one and in one embodiment aplurality of first y-guides 57 which are each connected to the bar 51and to one of the creasing elements 14 of the array 12. As such,coordinated rotation of first and second actuators 20 a and 20 c in acounterclockwise direction in FIG. 12 result in coordinated movement ofthe racks 21 and 39 in the x direction so as to cause the firstx-push/pull bar 51 to translate, push or move in the x direction andthus urge the left side of the bottom array 12 to the right. A secondx-push/pull bar 52 similarly extends in the y direction and is attachedat its first end to the top of one end of the inner rack 19 of the firstrack and pinion assembly 45 a and is attached at its opposite second endto the top of an end of the outer rack 41 of the second rack and pinionassembly 45 c, in each case by any suitable means such as an adhesive orone or more fasteners. The central portion of the second x-push/pull bar52 abuts a side, such as the right side in FIG. 12, of the bottom array12 and is attached to such side of array 12 by at least one and in oneembodiment a plurality of second y-guides 58 which are each connected tothe bar 52 and to one of the creasing elements 14 of the array 12.Coordinated movement of the racks 19 and 41, resulting from theforegoing coordinated rotation of first and second actuators 20 a and 20c in a counterclockwise direction in FIG. 12, causes the push/pull bar52 to translate, push or move in the x direction thereby bringing,sweeping or urging the entire right side of the bottom array 12 to theleft or first x-push/pull bar 51.

In a similar manner, a first y-push/pull bar 53 and a second y-push/pullbar 54 may be coupled to and extend between the rack and pinionassemblies 45 b and 45 d. More specifically, the first y-push/pull bar53 is attached at a first end to the top of one end of the outer rack 26of the third rack and pinion assembly 45 b and is attached at itsopposite second end to the top of an end of the inner rack 38 of thefourth rack and pinion assembly 45 d, in each case by any suitable meanssuch as an adhesive or one or more fasteners. The central portion of thebar 53 abuts a side, such as the front side in FIG. 12, of the bottomarray 12 and is attached to such side of array 12 by at least one and inone embodiment a plurality of first x-guides 55 which are each connectedto the bar 53 and to one of the creasing elements 14 of the array 12. Assuch, coordinated rotation of third and fourth actuators 20 b and 20 din a counterclockwise direction in FIG. 12 result in coordinatedmovement of the racks 26 and 48 in the y direction so as to cause thefirst y-push/pull bar 53 to translate, push or move in the y directionand thus urge the front of the bottom array 12 to the rear. The secondy-push/pull bar 54 similarly extends in the x direction and is attachedat its first end to the top of one end of the inner rack 28 of the thirdrack and pinion assembly 45 b and is attached at its opposite second endan end to the top of the outer rack 46 of the fourth rack and pinionassembly 45 d, in each case by any suitable means such as an adhesive orone or more fasteners. The central portion of the second y-push/pull bar54 abuts a side, such as the back side or rear in FIG. 12, of the bottomarray 12 and is attached to such side of array 12 by at least one and inone embodiment a plurality of second x-guides 56 which are eachconnected to the bar 54 and to one of the creasing elements 14 of thearray 12. Coordinated movement of the racks 28 and 46, resulting fromthe foregoing coordinated rotation of third and fourth actuators 20 band 20 d in a counterclockwise direction in FIG. 12, causes thepush/pull bar 54 to translate, push or move in the x direction therebybringing, sweeping or urging the entire back side of the bottom array 12towards the front or first y-push/pull bar 53. Third rack and pinionassembly 45 b and fourth rack and pinion assembly 45 d are positionedhigher in the z plane relative to bottom plate 4, and first y-push/pullbar 53 and second y-push/pull bar 54 mounted to and extending betweenassemblies 45 b and 45 d are positioned higher that first x-push/pullbar 51 and second x-push/pull bar 52 so that the travel of they-push/pull bars 53 and 54 does not interfere with the travel of thex-push/pull bars 51 and 52.

One or more guides coupled to the intermediate portions of the bottomarray 12 may be provided for facilitating the uniform expansion andcontraction of the bottom array 12 in the x and y directions. In oneembodiment, a plurality of the first x-guides 55 may be slidably coupledto first y-push/pull bar 53 and a plurality of the second x-guides 56may be slidably coupled to second y-push/pull bar 54. A first x-slidebar 59 a can be provided on or mounted to the first y-push/pull bar 53for slidably carrying the first x-guides 55, which can each be slidablycoupled or carried by the first x-slide bar by any suitable means suchas a bearing. Similarly, a second x-slide bar 59 c can be provided on ormounted to the second y-push/pull bar 54 for slidably carrying thesecond x-guides 56, which can each be slidably coupled or carried by thesecond x-slide bar by any suitable means such as a bearing. Respectivepairs of first x-guides 55 and second x-guides 56 can be secured toopposite ends of certain of the columns of creasing elements 14 of thebottom array 12. In this manner, one or more of the first x-guides 55and second x-guides 56 may slide or travel over or on respective x-slidebars or rails 59 a, 59 c when the array 12 is contracted or expanded inthe x direction. In one embodiment illustrated in the drawings and shownfor example in FIG. 12, a pair of guides 55, 56 is respectively securedto the bottom and top of each of the left-most column of creasingelements 14, the right-most column of creasing elements 14, a leftintermediate column of creasing elements 14 and a right intermediatecolumn of creasing elements 14.

In a similar manner, a plurality of the first y-guides 57 may beslidably coupled to first x-push/pull bar 51 and a plurality of thesecond y-guides 58 may be slidably coupled to second x-push/pull bar 52.A first y-slide bar 59 d can be provided on or mounted to the firstx-push/pull bar 51 for slidably carrying the first y-guides 57, whichcan each be slidably coupled or carried by the first y-slide bar by anysuitable means such as a bearing. Similarly, a second y-slide bar 59 bcan be provided on or mounted to the second x-push/pull bar 52 forslidably carrying the second y-guides 58, which can each be slidablycoupled or carried by the second y-slide bar by any suitable means suchas a bearing. Respective pairs of first y-guides 57 and second y-guides58 can be secured to opposite ends of certain of the rows of creasingelements 14 of the bottom array 12. In this manner, one or more of thefirst y-guides 57 and second y-guides 58 may be adapted to slide ortravel over or on respective y-slide bars or rails 59 b, 59 d when thearray 12 is contracted or expanded in the y direction. In one embodimentillustrated in the drawings and shown for example in FIG. 12, a pair ofy-guides 57, 58 is respectively secured to the left and right of each ofthe top-most row of creasing elements 14 and the bottom-most row ofcreasing elements 14. The plurality of x-guides 55, 56 may extendrelative to the y-push/pull bars in a first direction along the z axis,for example in an upward direction, for attaching to the respectivecreasing elements, while the plurality of y-guides 57, 58 may extendrelative the x-push/pull bars in a second opposite direction along the zaxis, for example a downward direction, for attaching to the respectivecreasing elements. In this manner, the x-guides and y-guides may slidealong respective rails or slide-bars without interfering with eachother. Interaction between the push/pull bars, guides and the creasingelements of the array will be described in further detail below.

As will be understood, during typical operation of the device, the pairof x-push/pull bars 51 and 52 generally move in a coordinated mannereither towards each other or away from each other from the rotation ofthe first and second pinion gears 17, 37, respectively driven by firstand second actuators 20 a, 20 c, which translate the respective sets ofouter and inner racks 21, 29 and inner and outer rack 19, 41. That is,during normal operation of the device, either the left or firstpush/pull bar 51 will move to the right while the right or secondpush/pull bar 52 will move to the left applying a generally inward orcompressive force to the opposite left and right sides of the array 12in the x direction. After such partial or complete contraction of thebottom array 12, the left or first push/pull bar 51 will move to theleft while the right or second push/pull bar 52 will move to the rightapplying a generally outward or tensile force to the opposite left andright sides of the array 12 in the x direction so as to pull the pullthe creasing elements 14 apart thus expand the array 12. In a mannersimilar to the discussion with respect to x contraction and expansion ofbottom array 12, coordinated movement of the racks 26, 24 and racks 28,46, driven respectively by pinions 27, 47 and actuators 20 b, 20 d, maysimilarly drive or sweep the longitudinal push/pull bars 53 and 54towards or away from each other such that they collapse or expand thebottom array 12 in the y direction. In one embodiment, such operation,as discussed below, results in either one-to-one contraction orone-to-one expansion of the creasing elements 14 in the bottom array 12in both the x and y directions when viewed in plan, for example asillustrated in FIG. 12, and in one embodiment the movement of the array12 in the x direction is coordinated with the movement of the array 12in the y direction such that the contraction or expansion in the xdirection is one-to-one with the contraction or expansion in the ydirection. Guides 55-58 serve to secure the respective bars 53, 54, 51,52 to the sides of the array, to facilitate even expansion andcontraction of the array and to minimize unwanted movement or distortionof all or any portion of the array along the z axis. Although in theillustrated embodiment the rack and pinion assemblies 42, 45 are adaptedto generate coordinated movement of respective pairs of push/pull bars,for example bars 51 and 52 move in unison and bar 53 and 54 move inunison, other actuation assemblies may be implemented to allow eachindividual push/pull bar to traverse its respective directionindependently. For example, instead of rack and pinion gears, eachindividual push/pull bar may be coupled to a separate actuator, thuseach push/pull bar may be individually driven to cause one or more ofthe sides of the arrays to move to a different extent than other sidesof the array.

In one embodiment, top array 10 is substantially identical to bottomarray 12, and the actuation assembly 22 for the top array 10 issubstantially identical to the actuation assembly 22 for the bottomarray 12. In one embodiment, first through fourth top actuators 18 a-18d are substantially identical to respective first through fourth bottomactuators 20 a-20 d and are respectively coupled to first through fourthrack and pinion assemblies or other suitable gear mechanisms 42 a-42 dthat are substantially identical to respective first through fourthbottom rack and pinion assemblies 45 a-45 d. In one embodiment, the topactuators 18 a-d and rack and pinion assemblies 42 a-d are aligned orregistered opposite the respective bottom actuators 20 a-d bottom rackand pinion assemblies 45 a-d, as shown for example in FIG. 3. In oneembodiment the top actuation assembly 22 further includes x and ypush/pull bars and guides substantially identical to the x and ypush/pull bars and guides discussed above with respect to the bottomarray 12. The top actuation assembly 22 can operate with respect to thetop array 10 in substantially the same manner as discussed above withrespect to the operation of the bottom actuation assembly with respectto the bottom array 12. Like reference numerals have been used herein todescribe and identify like components of top actuation assembly 22 andbottom actuation assembly 22.

Other form factors, assemblies or mechanisms for providing the desiredhorizontal motion of the arrays, for example along the x and ydirections, may be used. In this regard, other assemblies or mechanisms,for example pulleys and drive belts, may be used in place of or incombination with gears for transmitting the motion generated by thepower generation components, for example by actuators 20 or such othersuitable pumps, motors or pistons, of the actuation assembly 22. In someembodiments for example, x and y actuation or movement of the bottomarray 12 may be driven directly by one or more electrical motors suchthat the actuation assembly 22 does not include any gears, such as rackand pinion assemblies 42 and 45, or pulleys.

As can be observed in FIG. 2, the first or top array 10 and the secondor bottom array 12 are disposed such that rows of respective creasingelements 13, 14 are aligned in the y axis, while as can be seen fromFIG. 3 the top array 10 and the bottom array 12 are disposed such thattop and bottom columns 31, 32 of respective creasing elements 13, 14 arenot aligned in the x axis, as will be described in greater detail below.That is, as shown in FIG. 2, each of the plurality of first or topcolumns 31 of creasing elements 13 is offset to either the right or leftof each of the plurality of second or bottom columns 32 of creasingelements 14. In one embodiment, the top array 10 has one less column 31than the bottom array 12 (see FIG. 2). As shown in FIG. 3, each of theplurality of first or top rows 33 of creasing elements 13 is in linewith each of the plurality of second or bottom rows 34 of creasingelements 14. In one embodiment, the number or rows 33 in the top array10 is equal to the number of rows 34 in the bottom array 12. Thecreasing elements 13, 14 of each array 10, 12 may be regularly spacedrelative to each other, such that the relative spacing between adjacenttop columns 31 and between adjacent bottom columns 32, as well as theoffset between adjacent top and bottom columns 31, 32 may be the same,that is equal spacing between columns, as well as equal offset distancesbetween top and bottom columns, as shown in FIG. 2. Similarly, therelative spacing between adjacent top rows 33 may and between adjacentbottom rows 34 may be the equal.

In some examples, the columns of creasing elements of one of the arrays,for example the columns 31 of the first array 10, may be substantiallycentered between the columns of the other array, for example the columns32 of the second array 12. In some examples, the creasing elements maynot be regularly spaced in that some columns of creasing elements may becloser together than other columns of creasing elements and thereby theapparatus being operable to achieve different spacing between theresulting cells of the folded structures as will be further describedand appreciated in view of the present disclosure. As can be observed inFIG. 3, at some stages of the operation of apparatus 1 respective rows33, 34 of creasing elements are aligned in that a first or top row 33 ofcreasing elements 13 is in the same x-z plane as a corresponding secondor bottom row 34 of creasing element 14. However, as each of the top andbottom creasing arrays 10, 12 have their own independent actuationassemblies 22, each of the top and bottom arrays 10, 12 can move, forexample expand or contract, relative to each other and independent ofeach other in the x-y plane. Further, during certain stages of operationin some embodiments, the rows 33 of creasing elements or foldingelements of the first array 10 may or may not be aligned with rows 34 ofthe creasing elements or folding elements of the second array 12. Inaddition, the independent actuation assemblies 22 permit the secondarray to expand or contract in the x direction independently of anyexpansion or contraction of the array in the y direction.

As discussed above, the apparatus 1 may include one or more controllersoperatively coupled to the one or more of the actuation devices orassemblies 5 of apparatus 1, for example actuators 8, 18 and 20. The oneor more controllers (not shown) may be programmable to translate, usingthe actuation assembly 22, the arrays 10, 12 of creasing elements 13, 14according to a predetermined sequence of directions and steps to achievethe folding of the medium.

An exemplary foldable medium 60, and three dimensional support structure61, which may be formed using the apparatus and methods disclosedherein, are now described with reference to FIGS. 5-10. Various threedimensional support structures can be formed using the systems andmethods disclosed, examples of which are described in U.S. Pat. No.7,762,938 to Gale, which patent is incorporated herein by this referencein its entirety for any purpose. In some examples, three dimensionalstructures may be formed by folding one or more sheets of a flexiblematerial, for example folding medium 60, into a variety of patterns. Theflexible material or medium 60 may be paper, or other celluloseproducts, metal, plastic, composite or other materials. The material 60may be of varying grade and thickness, and may be selected from avariety of currently commercially available or later developed productsbased upon user preferences.

In some examples, a tessellation of generally rectangular foldedregions, for example cells 63, is defined, as will be further described.However, in some examples, substantially any shapes or patterns can beachieved depending on the desired three dimensional support structureand particular implementation of individual creasing elements 13, 14 andarrays 10, 12 of creasing elements utilized. In some examples, the arrayor tessellation of cells may define a regular pattern, or in examples,the cells may be irregularly arranged. Some cells may have a differentsize than other cells within the same tessellation. For example, groupsof narrow cells may be interspersed between groups of wider cells suchthat additional stiffness or rigidity is imparted to the foldedstructure in the regions where the narrow cells are located. Othervariations will be appreciated in light of the present disclosure andmay be implemented without departing from the scope of the presentinvention.

In some examples, the three-dimensional support structures 61,interchangeably referred to as folded structures herein, may be used inthe manufacture and composition of packaging materials and other supportstructures, used for example in fuselages, wings, bulkheads, floorpanels, construction panels, refrigerators, ceiling tiles, intermodalcontainers, and seismic walls. For example, the folded three-dimensionalsupport structures of the present invention can be used in place of orin addition to conventional core materials, such as foam core orhoneycomb core materials used in certain sandwich structures. However,other three dimensional structures for other applications can beimplemented according to the present disclosure and additionaladvantages to the ones described will be appreciated in light of thepresent disclosure.

As will be described in further detail below, the folded structures 61according to the present disclosure may be formed by folding the foldingmedium 60 in multiple directions so as to form vertical structures inthree planar orientations, namely, the x, y and z-axes. In someexamples, the three-dimensional structures are formed from a singlesheet of material or folding medium 60 which is folded into a repeatingpattern of cells 63 when viewed both from a first side or top, as shownin FIG. 7, and from a second side or bottom, as shown in FIG. 8. Each ofthe cells 63 is formed by and includes first and second spaced-apartendwalls 72, 74 and first and second sloped sidewalls or facets 76, 78spanning between the endwalls. In one embodiment, the first and secondspaced-apart endwalls 72, 74 of the folded structure lie parallel to thex-z plane, while the first and second sloped sidewalls 76, 78 aredisposed at an angle to the y-z plane and the x-z plane (see FIGS. 7 and8).

Each of the endwalls 72, 74 includes at least two plies of the material60 and each of the sidewalls 76, 78 includes at least a single ply ofthe material 60. In the embodiment of the folded structure 61illustrated herein, each of the endwalls 72, 74 is formed of two pliesof material 60 and each of the sidewalls 76, 78 is formed from a singleply of the material 60. First and second sidewalls 76, 78 of adjacentcells 63 are adjoined at a folded edge 80. The cells 63 are furtheraligned so that the first endwall 72 of one cell 63 from the repeatingpattern abuts the second endwall 74 of an adjacent cell 63 from therepeating pattern to form at least a four-ply wall 82 of the material60. When structure 61 is viewed from a first side, as shown in FIG. 7,the repeating cells 63 define a first surface 62 having a trough orvalley 86 therein, and when the structure is viewed from an oppositesecond side, as shown in FIG. 8, the repeating cells 63 define a secondsurface 64 having a trough or valley 86 therein. The first and secondsurfaces 62, 64 are each planar and parallel to the x-y reference planeof the three dimensional structure 61 and to each other. The foldingmedium 60, when folded into the desired pattern of repeating cells 63,defines a pattern of rails 65, which may be used to support and/or forattachment of an optional first liner (not shown) on first surface 62and an optional second liner (not shown) on second surface 64. That is,a first plurality of rails 65 a is formed on the first surface 62 and asecond plurality of rails 65 b is formed on the second surface 64. Thefirst and second plurality of rails 65 a, 65 b in combination with therespective folded edges 80 of such surfaces 62, 64 form first and secondspaced-apart grid like patterns which lie in parallel x-y planes.Accordingly, one or more optional liners may be supported to and/orattached to the folded structure along the grid like patterns. Thus, oneor more optional lines may be adapted to lie generally in-plane with thesurfaces 62, 64, and parallel to the x-y reference plane.

In some examples, the pattern of repeating cells 63 includes thefour-ply wall structure 82 as described above, and a repeating patternof ascending facets or sloped sidewalls 78 and descending facets orsloped sidewalls 76 (see FIGS. 6-8). As depicted in FIG. 6 showing apartially folded medium and in FIGS. 7 and 8 showing a fully foldedstructure, the plurality of adjoining sloped sidewall 76, 78, whenviewed along the y direction, alternate in a pattern of ascending anddescending sloped sidewalls relative to the x-z plane. Adjacentascending facet or sloped sidewall 78 and descending facet or slopedsidewall 76 form a plurality of apexes or peaks 80 and a plurality oftroughs or recesses 86. Adjoining facets 76 and 78 meet at ridge or peak80 to define the peak or top fold 80, and also meet at the bottom oftrough or valley, to define the trough fold 86. The peak fold 80 onfirst surface 62 corresponds to the trough fold 86 on second surface 64,and the trough fold 86 on first surface 62 corresponds to the peak fold80 on second surface 64. Similarly, the peak fold 80 on second surface64 corresponds to the trough fold 86 on first surface 62, and the troughfold 86 on second surface 64 corresponds to the peak fold 80 on firstsurface 62.

The peak folds 80 and recess folds 86 are generally parallel to eachother and are generally perpendicular to the rails 65. When structure isviewed from the first side, for example as in FIG. 7, the peak folds 80extend in a first x-y plane and the recess folds extend in a second x-yplane. The rails 65 generally span along the x direction, while theorthogonal folds 80 and 86 generally span the y direction. The grid-likepattern defined by the rails 65 and orthogonal folds 80 may provide anincreased surface area for supporting an object on the structure 61.Furthermore, the combination of four-ply wall structures 82 providedgenerally perpendicular to sloped facets 76, 78 of the folded structuremay provide enhanced structural rigidity and stability of the foldedstructure 61 which may be advantageous when using said folded structuresto support various objects thereon. A substantially similar pattern ofpeaks 80 and troughs 86, and a similarly repeating pattern of cells 63is defined when viewing the structure 61 from the first side, as in FIG.7, or the second side, as in FIG. 8. As will be appreciated, theeffectively continuous rails 65 created by the plurality of four-plywalls 82 and folds 80 and 86 provide substantial strength and rigidityto the three dimensional structures 61 formed using the systems andmethods described.

To aid in understanding of the folding methods and apparatus accordingto the present disclosure, a folding medium 60 will be described infurther detail with reference to FIG. 5, which shows a plan view of anexemplary unfolded sheet of material or folding medium 60 for use informing durable support structures according to examples describedherein. To form the structure described above, the material 60 may befolded from a substantially flat, planar state. The medium 60 hereinchanges in three directions as it is folded from its planar, unfoldedstate shown in FIG. 5, into the three-dimensional form shown in FIGS. 7and 8. Specifically, the medium 60 increases in height, that is alongthe z-axis, while decreasing in both length, that is along the y-axis,and in width, that is along the x-axis. The folding medium 60 may beprovided as a generally rectangular sheet of material, or it may haveany other desired shape such as circular, oval, trapezoidal, triangular,or other complex profiles as desired or as may be suitable for theparticular application. The sheet of material 60 may include a firstlongitudinal edge 66, a second longitudinal edge 67, a first side edge68, and a second side edge 69. The first longitudinal edge 66 and secondlongitudinal edge 67 extend between the first 68 and second 69 sideedges together such edges 66-69 define the plan profile of the foldingmedium 60.

To facilitate the folding of the sheet of material or folding medium 60,a plurality of creases or fold lines 70 may be formed prior to or whilethe folding medium 60 is being folded. In one embodiment, the creases orfold lines 70 may be formed by scoring or otherwise weakening thefoldable medium according to the desired pattern prior to the folding ofthe medium. For example, perforations, detents, or other features may beimparted along a predetermined pattern on one or both of the surfaces ofthe folding medium 60 before the folding process beings. In oneembodiment, all of the fold lines 70 along which the medium will befolded may be pre-defined for example by scoring or perforating themedium 60 using a laser along a portion or all of such fold lines 70. Inone embodiment, only some of such fold lines 70 are be pre-definedbefore the folding process and other such fold lines 70 are formedduring the folding process. Any combinations of scoring or pre-formingthe fold lines may be used as may be suitable for a particular foldingmaterial or application. In one embodiment, the unfolded medium 60 maycontain a repeating pattern of scores or creases 70 which include aplurality of intersecting crease paths 71. As the folding medium 60 isbeing folded into a three dimensional structure, portions of the mediumwill displace upward relative to a reference plane of the unfoldedmedium, that is the x-y plane, while other portions will displacedownward relative to the reference plane or remain in the referenceplane. That is, the contour of the medium 60 when formed into a threedimensional structure 61 will include peaks and troughs defined alongthe plurality of creases or fold lines 70 as the respective portions ofthe medium 60 fold up and down relative to the plane of the unfoldedmaterial.

In broad terms, fold lines 70 of the folding medium 60 include aplurality of first crease paths 73, 75, as examples, extending parallelto each other and a plurality of second crease paths 77, 79 alsoextending parallel to each other and intersecting the first crease paths73, 75. Each first crease path 73, 75 is formed from a plurality offirst path segments 81. Each plurality of first path segments 81associated with each one of the first crease path 73, 75 are generallyaligned form a straight line along the x direction. As will beunderstood, the xyz reference frame referred to herein is used for thepurposes of facilitating the description and relative arrangement ofcomponents and is not to be taken in a limiting sense.

Each second crease path 77, 79 is formed from a repeating pattern offirst and second chevron segments or angled legs 83, 85 and a straightline or leg 87 extending from a free end 88 of one of the first andsecond angled legs 83, 85, for example the free end 88 of the secondchevron segment 85 shown in FIG. 5. That is, unlike the plurality offirst crease path 73, 75, which follow a generally straight line, eachof the second crease paths 77, 79 follows a path defined by adjoiningangled legs 83, 85 and straight lines or legs 87. As will be understood,the term “legs” used to describe the imaginary fold lines or scoringpattern of the planar structure described herein is so designated fordiscussion purposes only and is not to be viewed in a limiting sense.Any similar or suitable designation would be acceptable for the purposesprovided.

In one embodiment, the two angled legs or chevron segments 83, 85 may beequal in length and may form an angle of about 120° . That is, a firstangle 89 defined by two adjoining angled legs 83, 85 may in someembodiments be equal to 120 degrees. Other angles may be used to providedifferent folding patterns or achieve different folded structures. Inone embodiment, pairs of adjoining chevron legs or segments 83 and 85have equal lengths, however in some embodiments some pairs may havedifferent lengths. That is, a first pair 91 of chevron legs or segmentsmay have a first length, while the next or second pair 92 of chevronlegs, which is separated from the first pair 91 by a straight linesegment 87 joined at one end to first pair 91 and at its other end tosecond pair 92, may have a second length which is different from thefirst length. Each of the legs 83, 85 in a pair of angled legs maygenerally have the same length, for example generally defining a topportion of an equilateral triangle.

A plurality of straight lines or legs 87 extend between non-adjoiningends of each chevron segments or angled legs 83, 85. The line 87 may beof any length. The length of line 87 may be the same as the length ofthe angled legs 83, 85, or it may be a length which is different thanthe length of such angled legs. Similarly, the first path segments 81forming the first crease paths 73, 75 may be of any length as may bedesired. The length of the segment 81 may be the same as any one of thelengths of lines 87, or angled legs 83, 85, or it may be a differentlength. As will be appreciated in light of the examples described, thelength of segment 81 in combination with the angle of sloping facets 76,78 may generally define the overall thickness, for example the height inthe z axis, of the final folded three-dimensional structure 61.

As shown in FIG. 5, the plurality of second crease paths 77, 79intersect the plurality of first crease paths 73, 75. The medium 60 isfoldable along the first and second crease paths 73, 75, and 77, 79 toform three dimensional support structure 61 according to the presentdisclosure. One embodiment of the structure 61 formed from medium 60,shown unfolded in FIG. 5, is shown in a partially assembled state inFIG. 6 and in a fully folded state in FIGS. 7 and 8.

In one embodiment of the folding process of the present invention, andas shown in FIG. 6 for example, during an intermediate folding stage oneof the plurality of second crease paths, 79 for example, is foldedupwards, while the next of the plurality of second crease paths in the xdirection, 79 for example, is folded downwards. This is repeated alongthe length of the side edges 68, 69 to form a pleating or accordion-likestructure, as shown in FIG. 6. Due to the discontinuous nature of eachof the second crease paths 77, 79, which as discussed above can beformed by a continuing sequence of first and second angled legs 83, 85and a straight leg 87, the accordion-like pleating does not follow astraight line but instead follows a zigzagging path along the creasepaths. This zigzagging of the second crease paths 77, 79, 79, as shownin FIGS. 5 and 6, further facilitates the folding of the medium 60 intoa compact shape. While such a zigzagging pattern has certain advantages,such a configuration is not to be taken in a limiting sense and otherconfigurations or folding patterns can be provided. In one embodiment,the folding medium may be generally rectangular, such that all foursides, for example the longitudinal edges 66, 67 and side edges 68, 69comprise straight line segments. Creases or fold lines 70 may be definedon such a generally rectangular medium, without requiring that themedium be cut to any particular shape or have any particular perimeterprofile, to provide the desired folding pattern.

Each second crease path 77 is foldable in an opposite direction from theadjacent second crease path 79. This results in the formation of analternating pattern of ridges or peaks 80 and valleys or troughs 86 asthe sheet of material or folding medium 60 is folded. For example, thelowermost second crease path 77 in FIG. 5 can serve as a trough 86 ofthe folded structure 61, when viewed from the first side such as in FIG.7, and the adjacent second crease path 79 can serve as a peak or peakfold 80 when the structure 61 is so viewed from the first side. The nextadjacent second crease path 77 in the x direction can serve as a trough86 or valley fold 86. Each of the first crease paths 73, 75 are straightlines extending between the peaks 80 and troughs 86 of adjacent secondcrease paths 77, 79, and thus between the first and second longitudinaledges 66, 67 of the folding medium 60. Certain adjacent crease paths 73,75 form a pattern of facets 76, 78 on a surface of the folded structure61. At least some of the first crease paths 73, 75, and in oneembodiment all of the crease paths 73, 75,follow a zigzagging pattern orsequential ascending and descending lines to form a plurality ofalternating ascending and descending paths 90 that extend between firstand second longitudinal edges 66, 67 and define the ascending anddescending facets 76, 78 of the folded structure. A first plurality ofadjacent first crease paths 93, 94, included in paths 90, connect therespective opposite ends of adjacent straight lines 87 and follow theascending and descending contour of adjacent cells 63. Each facet 76, 76is bounded by a portion of adjacent first crease paths 93, 94 and a pairof adjacent peak folds 80 and valley folds 86. A second plurality of thefirst crease paths 95, 96, included in paths 90, respectively connectthe adjoined ends of a first pair of adjacent angled legs 83, 85 and theadjoined ends of a second pair of adjacent angled legs 83, 85, and eachrespectively fold into and become part of a pair of adjacent rail orwall 65 of the support structure 61.

In one embodiment, and as depicted in FIGS. 7 and 8, each portion 108 ofrails 63 spanning between adjacent cells 63 of the folded structure mayinclude at least a pair of two-ply segments 97, which form the end walls72, 74 and thus the at least four-ply wall structure 82 between suchadjacent cells 63. In one embodiment, each of the two-ply segments 97may extend into the adjacent portion 108 of the rail 65, that is theportion 108 between the adjacent cells along the x axis, and thussections of the rail 65 may comprise 8-ply structure. Otherconfigurations may be achieved using different crease paths, for examplevarying the length of the first path segments 81, chevron segments 83,85 and straight line or leg segment 87, as well as varying the anglesbetween such segments, for example the angle 89 between adjoined chevronor angled leg segments 83, 85. In one embodiment, when the length ofangled segments 83, 85 is greater than the length of line segment 87,the resulting rail 65 may include portions which have more than fourplies. In one embodiment, some portions of the rail 65 may have fewerthan four plies, for example two plies.

The folding process will be further described with reference to one of aplurality of regions 98 of the tessellated folding medium 60,illustrated in FIG. 6 and depicted in greater detail during stages ofthe folding process in FIGS. 9 and 10. As shown in a partially foldedstate in FIGS. 6 and 9, in one embodiment a portion of the foldingmedium 60 comprises a first leg or chevron segment 83 and a second legor chevron segment 85 forming a first angled segment or chevron. Thefirst leg 83 and second leg 85 are preferably of equivalent length. Afirst angle 89 exists between the first leg 83 and the second leg 85.The angle 89 preferably measures about 120° in the flat unfolded state.A third leg or straight line 87 extends from a free end 88 of the secondleg 85 and another third leg 87 extends from a free end of the first leg83. The length of third legs 87 may be of any length to accommodatemanufacturing preferences, thus the third leg may be equal to, shorteror longer than the first and second legs 83, 85. The third leg 87adjoining first chevron segment 83 extends at a second angle 99 from thefirst chevron segment 83 and the third leg 87 adjoining second chevronsegment 85 extends at a third angle 100 from the second chevron segment85. Each of the angles 99, 100 which may be approximately 150° in theflat unfolded state of the folding medium, illustrated for example inFIG. 5. In one embodiment, the angles 89, 99 and 100 may be different insize. In one embodiment, some or all of angles 88, 99 and 100 may be thesame in size.

A set of first segment or leg 83, second segment or leg 85 and one ofthe adjoining third segments or legs 87, for example the leg 87adjoining first segment 83, define a repeating pattern 109 along thelength of the first crease paths 77, 79, and thus the length of foldedstructure 91 (see FIGS. 6, 9 and 10). Each such repeating pattern 109 isconnected by a plurality of first path segments 81 to an adjacentpattern 109 of adjoined legs 87, 83, 85, spaced apart along the x axisby such plurality of parallel first path segments 81, to define arepeating pattern of facets 101, 102, and 103 that extend along thelength of folded structure 61. A fourth angle 111 is defined by theintersection of each first path segment 81 and the free end 88 of eachfirst chevron segment 83, and a similar fourth angle 111 is defined bythe intersection of each first path segment 81 and the free end 88 ofeach second chevron segment 85 (see FIG. 5). In one embodiment, thefourth angle 111 may be approximately 60 degrees in the flat unfoldedstate of the folding medium, illustrated for example in FIG. 5. In oneembodiment, for example depending on the size of angles 89, 99, and 100,the fourth angle 111 may be other than 60 degrees. A fifth angle 113 isdefined by the intersection of the straight horizontal line segment 87and the adjoining vertical line segment 81, and may be approximately 90degrees, as illustrated in FIG. 5. Angle 113 generally remains at 90degrees when the structure 61 is fully folded, as illustrated withregion 98 shown in FIG. 10. As the medium 60 is folded the angles 99 and100 which may originally be obtuse angles may collapse or reduce toapproximately 90 degrees, and angle 89 between adjoining angled legs 83,85 which may originally be obtuse an obtuse angle may collapse or reduceto zero, in the fully folded structure 61 having the grid-like patternor tessellation of cells 63.

In this manner, the repeating pattern of facets 101, 102 and 103,defined by various combinations of legs or segments 87, 83 and 85 asdescribed above connected by a plurality of first path segments 81,repeat along both the y-axis and the x-axis (see FIGS. 5-6). Any numberof repeating pattern of facets 101, 102 and 103 may be used to form thethree-dimensional support structures herein. Preferably, the size of thethree-dimensional support structure is defined by the number of facets101, 102 and 103, the size of such facets, or the legs 87, 83 and 85creating the facets, and the desired size of the support structure to becreated by the folded tessellated medium. Adjacent pairs of therepeating pattern 109 of legs 87, 83 and 85 interconnected by aplurality of first path segments 81 spaced apart along the y axis definea repeating pattern of longitudinal regions or strips 110, 112 of thefolding medium 60 which extend along both the length and width of themedium 60. When the medium 60 is folded, one or first region or strip110 slopes upwards as it extending in the x direction and the adjacentsecond region or strip 112 slopes downwards as it extends in the xdirection, as shown in FIG. 10, so as to provide a pleated oraccordion-like portion of one embodiment of the folded support structureof the present invention.

As described herein, the scores or fold lines that can be preformed inthe medium 60 for forming the legs or segments of the foldable medium,for example legs or segments 87, 83, 85, 81, serve to assist in foldingthe medium 60 into the support structure of the present invention. Thefold lines depicted herein, for example in FIGS. 5 and 6, are providedfor illustration purposes, and it is understood that in some embodimentsno such preformed scores fold lines are present on the sheet ofmaterial. In this regard, folds can be formed during the folding processalong at least some of the imaginary fold lines described above, forexample along some or all of legs or segments 87, 83, 85, 81. As themedium 60 is folded, for example as shown in FIG. 6, the scores or foldlines cooperate to form a series of peaks 80 and valleys 86 in themedium 60 ultimately resulting in the repeating pattern of cells 63described herein. In one embodiment, where scoring or other weakling ofthe material or foldable medium 60) is provided prior to the foldingprocess, the scoring may be provided on one or both of the surfaces ofthe foldable medium 60. For example, scoring may be provided only on atop surface of the medium for a select set of the plurality of crease orfold lines 70, and scoring may be provided on the bottom surface of themedium for the remaining crease or fold lines 70. As will beappreciated, providing scoring selectively on the top or bottom surfaceof the material may guide the direction of folding, in that the mediummay naturally fold in the direction of the weakened surface.

In one embodiment of the folding process of the invention, the foldablemedium 60 may be folded in the desired pattern of cells 63 as follows. Apleating of the medium may be obtained by folding consecutive oradjacent second crease paths 77, 79 in alternating upward and downwarddirections. Simultaneously or at a different time, which may be prior toor after the pleating step, the medium may also be folded along firstcrease paths 73, 75. As the folding medium is folded, the angle 89decreases in size until it becomes approximately zero degrees, at whichpoint, a first endwall 72 of one cell abuts or lies adjacent to a secondendwall 74 of the adjacent cell forming the four ply structure 82. Theangles 99 defined by each straight line segment 87 and the adjoiningangled leg 83 and the angles 100 defined by each such straight linesegment 87 and the adjoining angled leg 85 both also decrease as thestructure is folded, and in one embodiment of the structure 61illustrated in FIGS. 7-8 is approximately 90 degrees. In the foldedconfiguration, each of the segments 87 coincides with a peak fold 80 orvalley fold 86. Accordingly, in the folded configuration, the resultingangles 107 between the segment 87 and each of the adjoining segments 83and 85, which define the edges of the four ply wall structure 82, isapproximately 90 degrees. In this manner, a repeating pattern of cells63 is formed and may be arranged in a generally grid like or tessellatedmanner. As will be appreciated, the resulting folded structure hasoverall dimensions, for example length and width, which are less thanthe dimensions of the flattened unfolded medium. That is, as thethree-dimensional structure is formed from a single sheet of material,the dimensions of the resulting product decrease along the x and ydirection, while the dimension of the resulting product increases in thez direction, thus adding height to the structure.

Returning now to the exemplary apparatus and methods for forming thefolded structures of the present invention, the relative positioning,actuation and operation of the top and bottom arrays 10, 12 of creasingelements 13, 14 will now be described. In the exemplary apparatus 1,each array 10, 12 includes a plurality of respective creasing elements13, 14 arranged in respective columns 31, 33 and respective rows 32, 34and configured to be moveable along the x direction and the y direction.In addition, one or both of arrays 10, 12 may also be moveable in the zor vertical direction 15. Relative motion of the arrays 10, 12 and ofthe individual respective creasing elements 13, 14 will be furtherdescribed below with reference to an exemplary folding operation.

FIG. 14 shows a perspective view of a portion 12 a of the second orbottom array 12, depicted in FIGS. 1-4, in a fully expanded or firstposition. A corresponding top portion 10 a of the first or top array 10,in a fully expanded or first position, is shown along with the bottomportion 12 a in FIGS. 16-17, 19-20. For clarity of illustration andsimplification, only portions 10 a, 12 a of the arrays 10 and 12 areshown in FIGS. 14-17, 19-21, 23-24 and 28-30, however the exemplaryarrangements depicted and described herein may apply to any size arrayaccording to the present disclosure, for example the full arrays 10, 12shown in FIG. 1, or to arrays of any other size or arrangement selectedas may be desired.

It is appreciated that some or all of creasing elements 13 of top array10 can be substantially identical, and that some or all of creasingelements 14 of bottom array 12 can be substantially identical. In oneembodiment, illustrated in the above figures, all of creasing elements13, 14 are identical. Each individual creasing element 13, 14, which mayalso be referred to as a creasing member or a folding element or member,may be implemented as a generally elongate member, which may have arectangular transverse cross section (see FIGS. 14-15). It isappreciated that some or all of the creasing elements may be configuredto have substantially any transverse cross section, for example suchcreasing elements may be circular or oval in the transversecross-section such that the creasing elements are generally shaped asrods or other cylindrical members. Other form factors may be used asdesired for forming some or all of the creasing elements.

In one embodiment, each creasing element 13, 14 includes a first or topportion 150 and a second or body portion 151 (see FIG. 14 with respectto bottom array portion 12 a). The top portion 150 may be shaped to havea leading edge 122 which is configured to engage or fold the foldablemedium 60. The leading edge 122 may be shaped in any manner suitable toengage the sheet of material or folding medium 60 and facilitate thefolding of the sheet of material. For example, the leading edge 122 mayinclude a sharp or dull edge disposed at the top most end of the topportion 150. The leading edge may be continuous or segmented with one ormore spaces therein so as be noncontinuous. The leading edge 122 may beprovided with sharp puncture or scoring elements spaced along the edgefor scoring the medium 60 along a fold line 70 or otherwise facilitatingfolding of the medium at the portion engaged by the leading edge. Theleading edge 122 may be defined by two opposite sloping sides or faces124, 126 of the top portion 150 inclined at any suitable angle relativeto each other and sloping outwardly from and relative to leading edge122 to accomplish the desired folding of the medium. In one embodimentthe sloped sides 124, 126 are inclined at an angle of not greater than90 degrees relative to each other, and in one embodiment the slopedsides 124, 126 are inclined at an acute angle, for example 60, 45 or 30degrees, relative to each other. The leading edge 122 may be slightlyrounded so as to prevent or minimize risk of tearing or otherwisedamaging the material or medium 60 being folded. The sides or faces 128,130 extending between the sloping sides 124, 126 may be generallyparallel to each other, or they may be angled relative to one another,and in one embodiment extend at 90 degrees to the sides or faces 128,130. As shown in FIG. 14 for example, the top portion 150 of anexemplary creasing element 14 is shaped to resemble a gable in that ithas a generally triangular cross section in the x-z plane formed bysloping faces 124, 126 that are inclined relative to each other.

Body portion 151 of a creasing element can include a top, distal orupper section 170, a middle or central section 171 and a bottom,proximal or lower section 172, as shown in FIG. 14. The body portion 151of each creasing element 13, 14 may be shaped and configured in anymanner desired which accommodates coupling the body portion 151 of eachcreasing element of the respective array 10, 12 and which furtheraccommodates coupling the array to the actuation assembly 5. In oneembodiment, as discussed above, the creasing elements of each array arearranged in rows and columns such that each creasing element is adjacentto at least one and preferably a plurality of other creasing elements.For example in FIG. 14 with respect to bottom array 12, creasing element14 e is adjacent to and disposed between creasing elements 14 d, 14 falong the x direction and adjacent to and disposed between creasingelements 14 b, 14 h in the y direction.

Adjacent creasing elements can be connected together using suitablelinking assemblies which can permit expansion and contraction of columnsof creasing elements along the y axis and expansion and contraction ofrows of creasing elements along the x axis. In one embodiment, theexpansion and contraction of the creasing elements in the y axis isindependent of the expansion and contraction of the creasing elements inthe x axis. The linking assemblies may be configured such that allcreasing elements in a row 33 or 34 of creasing elements are moveabletogether in a first direction, for example along the y axis, and allcreasing elements in a column 31 or 32 of creasing elements are moveabletogether in a second direction, for example along the x axis. As such,the first direction and second direction can be orthogonal to eachother. In one embodiment (not shown) of creasing element arrayssubstantially similar to arrays 10, 12, the linking assemblies may beimplemented using x-guide rods and y-guide rods, where x-guide rodscouple rows 34 of creasing elements together and y-guide rods couplecolumns 32 of creasing elements together, in each case to permitexpansion and contraction of such creasing elements relative to eachother. For example, a first x-guide rod may couple the creasing elementsof a first row together such that the first row of creasing elementsmoves in unison in a first direction. A second x-guide rod may couple asecond or adjacent row of creasing elements such that the all creasingelements in the second row move in unison in the first direction. In anexemplary orthogonal orientation in which the second direction isperpendicular to the first direction, a first y-guide rod may couple allof the creasing elements in a first column 31 or 32 together, and asecond y-guide rod may couple all of the creasing elements in a secondcolumn 31 or 32 together. The y-guide rods may be disposed generallyperpendicularly to the x-guide rods an as such create a matrix of rodelements when viewed in plan, that is in the x-y plane. Individualcreasing elements may be provided at imaginary intersection points ofthe two rod elements. The x-and y-guide rods may be coupled toindividual creasing elements such that each individual creasing elementis able to move both in the x and y directions. For example, the x-guiderods may be provided in a first x-y plane, while the y-guide rods may beprovided in a second x-y plane offset from the first x-y plane along thez axis. The plurality of parallel x-guide rods may be so offset alongthe z direction above or below the plurality of parallel y-guide rodssuch that the movement of the x-guide rods along the x direction doesnot interfere with the movement of the y-guide rods along the ydirection.

In one embodiment, the linking assemblies, which may interchangeably bereferred to herein as expandable linking assemblies or directionallyexpandable linking assemblies, may be implemented using y-travel scissorassemblies 154 and x-travel scissor assemblies 152 for respectivelycoupling together columns 31 or 32 of creasing elements and rows 33 or34 of creasing elements. Each y-travel 154 and x-travel 152 scissorassembly, which can be made from any suitable material such as metal orplastic, includes a pair of scissor elements or links. For example, eachy-travel scissor assembly 154 may include a first y-scissor link 156 anda second y-scissor link 158 (see FIG. 14). The first and secondy-scissor links 156, 158 are pivotaly coupled together using a pivotmeans or joint that can include for example an x-center pivot element orpin 157. Each y-scissor link 156, 158 has a y-first end 160 and ay-second end 162. In one embodiment, the y-first end 160 of eachy-scissor link 156, 158 may be fixedly coupled to central section 171 ofthe body portion 151 of respective adjacent creasing element, forexample by using a y-fixed pivot element or pin 161. In one embodiment,the y-first end 160 of first y-scissor link 156 is coupled to one sideof its creasing element and the y-first end 160 of second y-scissor link158 is coupled to the opposite other side of its creasing element. They-second end 162 of each y-scissor link 156, 158 may be slidably coupledto central section 171 of the body portion 151 of the respectiveadjacent creasing element, for example using a y-moveable pin 163slidably disposed in a y-slot 165 provided on the central section 171and extending longitudinally in the z direction. In one embodiment, theslidable end 162 of each scissor link 156, 158 is below the pin 161 onthe central section 171 but on the same side of the creasing element asthe respective y-first end 160 of the link, however an alternatearrangement can be provided in which the slidable end 162 is providedabove the fixed end 160. In one embodiment, the y-first end 160 of eachy-scissor link 156, 158 may be slidably coupled to the respectiveadjacent creasing element 13, 14, and the y-second end 162 may befixedly coupled to the respective adjacent creasing element.Furthermore, in the present example a single y-travel scissor assembly154 is provided for coupling together each pair of adjacent creasingelements, however in one embodiment more than one, for example, two,three or more y-travel scissor assemblies may be included and similarlyconfigured. Each y-scissor link 156, 158 is longitudinally sized topermit the desired separation between adjacent creasing elements coupledtogether by such links during expansion of the respective array 10, 12in the y direction.

In a similar manner, each x-travel scissor assembly 152 may include afirst x-scissor link 153 and a second x-scissor link 155 (see FIG. 19).Similar to the y-travel scissor links 156, 158, each x-travel scissorlink 153, 155 has a x-first end 164 and a x-second end 166. In oneembodiment, the x-first end 164 may be coupled to the body portion 151using a x-fixed pin 167. In one embodiment, the x-first end 164 of firstx-scissor link 153 is coupled to one side of its creasing element andthe x-first end 164 of second y-scissor link 155 is coupled to theopposite other side of its creasing element. The x-second end 166 of thex-scissor links may be moveably or slidably coupled to the body portion151 using a x-moveable pin 169 extending through a x-slot 168 providedin the body portion 151 and extending longitudinally in the z directionon the body portion 151. The x-second end 166 of each link 153,155 isslidable coupled to the respective body portion 151 on the same side ofthe creasing element as the respective x-first end 164 of the link. Thefirst x-scissor link 153 and second x-scissor link 155 may be pivotallycoupled to each other using a x-center pin 159. Each x-scissor link 153,155 is longitudinally sized to permit the desired separation betweenadjacent creasing elements coupled together by such links duringexpansion of the respective array 10, 12 in the x direction. In oneembodiment, the y-scissor links 156, 158 are longer than the x-scissorlinks 153, 155 to permit greater expansion of the arrays 10, 12 in the ydirection than in the x direction. In the present example, first andsecond x-travel scissor assemblies are utilized for coupling togethereach adjacent pair of creasing elements in the x-z plane. First x-travelassembly 152 a is coupled to distal or upper section 170 of eachadjacent creasing element, above y-travel scissor assemblies 154, andsecond x-travel assembly 152 b is coupled to proximal or lower section172 of each adjacent creasing element, below y-travel scissor assemblies154. It is appreciated that any number of x-travel scissor assembliesmay be provided. In one embodiment, a single-travel scissor assembly maybe used for coupling together each pair of adjacent creasing elements.Further, it is appreciated that any arrangement of the scissorassemblies 152, 154 on the creasing elements, different from thearrangements discussed above, can be provided.

The pivotal joints 159 in combination with the moveable or slidablecoupling between at least one end 166 of the x-scissor links 153, 155and a respective portion of the adjacent creasing elements 13, 14 allowthe relative angle 180 between such scissor elements or links 153, 155to change (see FIG. 19). The change in angle 180 causes the distance 183along the x-axis between adjacent creasing elements 13, 14 to decreaseor increase. Similarly, the pivotal joints 157 in combination with themoveable or slidable coupling between at least one end 162 of they-scissor links 156, 158 and a respective portion of the adjacentcreasing elements 13, 14 allow the relative angle 181 between suchscissor elements or links 156, 158 to change (see FIG. 20). The changein angle 181 causes the distance 182 along the y-axis between adjacentcreasing elements 13, 14 to decrease or increase. In this manner, thelinking assemblies, for example scissor assemblies 152, 154 facilitateexpansion and collapsing or contraction of the arrays 10, 12 of creasingelements during the folding process.

The creasing elements 13, 14 can be made from any suitable material suchas metal, plastic or a ceramic material, and in one embodiment can bemade from a rigid such material. Not all of the creasing elements needbe made from the same material, for example some creasing elements canbe made from a rigid plastic, some other creasing elements can be madefrom metal and some other creasing elements can be made from a ceramicmaterial. In one embodiment, the top 150 and body 151 portions of eachcreasing element 13, 14 may be formed as a single unitary structure, forexample a monolithic component fabricated in one piece by molding ormachining, as examples. In one embodiment, each creasing element maycomprise a plurality of individual sub-components which are assembled toform the creasing element and assembled into each of the arrays 10, 12of creasing elements.

In one embodiment, an end portion 173 of the bottom section 172 of acreasing element 13, 14 may be provided with a sliding contact surfaceor bearing 175. In one embodiment, the end portions 173 may besufficiently spaced apart from and above the platforms 4, 6 such thatthe end portions 173 do not contact the platform at any time or duringoperation of the actuation or creasing assemblies 5, 7. In such anembodiment, the arrays of creasing elements may be generally describedas floating above the platforms 4 and 6. Additional rigidity and forcemay be obtained by allowing the imaginary bottom surfaces of each array10, 12 to contact the respective platforms 6, 4. In this regard, the endportion 173 of each creasing element 13, 14 may be lubricated and/orcoated with a slip agent, or other low frictional material, for examplea polymer. The end portion 173 may be fabricated using a material havinga low coefficient of friction, or the end portion 173 may be otherwiseconfigured for sliding and/or bearing contact with the platforms, forexample by using roller bearings or other conventional low frictionalbearing mechanisms. Various sliding or pivoting joints, such as thepivotal joints 157, 159, fixed pins 161, 167 and sliding pins 163, 169as well as surface of sliding contacts, for example surfaces of slots165, 168 adapted for receiving the sliding pins 163 and 169, may also belubricated, coated with or otherwise manufactured from materials whichprovide low frictional resistance and minimize wear of such slidingcomponents.

The specific embodiments of linking assemblies or expandable linkingassemblies described above, including rod elements and scissorassemblies 152, 154, are just two examples of the variousimplementations of interlinking of creasing elements that are possibleaccording to the present disclosure. It is appreciated that othervariations are possible which accomplish the desired linking of creasingelements such that all creasing elements in a given row 33, 34 ofcreasing elements may be moveable in unison in a first direction, andall creasing elements in a given column 31, 32 of creasing elements maybe moveable in unison in a second direction. In one embodiment,individual actuation of each creasing element 13, 14 may also beprovided if desired, and one or more controllers may be configured tocreate the coordinated movement of creasing elements 13, 14. Forexample, using a desired timing sequence, the plurality of push/pullbars 51-54 working in conjunction with the compliant linking assemblies,for example x-travel scissor assemblies 152 and y-travel scissorassemblies 154, may operate to cause the arrays 10, 12 to collapse orcontract along the x and y directions thereby forming folded structures61 according to the present invention (see FIGS. 12, 25-27).

An exemplary folding operation will now be further described withreference to FIGS. 16-31 to further illustrate the methods and apparatusof the present invention. Although some of such figures include onlyportions 10 a, 12 a of top and bottom arrays 10, 12, the discussionherein is applicable to the entire arrays 10, 12 and thus will referencethe entire arrays 10, 12 illustrated in FIG. 1 and other figures herein.Initially, a sheet of material 115, which may be configured as foldingmedium 60 and have a similar pattern of imaginary fold or crease linesas described above, may be placed between first or top leading edges 120of the first or top creasing elements 13 of the first array 10 andsecond or bottom leading edges 122 of the second or bottom creasingelements 14 of the second array 12, as shown in FIG. 17.

In one embodiment, the first array 10 and the second array 12 areinitially in a first relative position in which the respectiveindividual creasing elements 13, 14 are not interdigitated with eachother. Instead, the plane defined by the leading edges 120 of thecreasing elements 13 of the first array 10 is generally in the sameplane or spaced away from the plane defined by the leading edges 122 ofthe creasing elements 14 of the second array 12 (see FIGS. 16 and 17).In one embodiment, the first array 10 and the second array 12 may bespaced apart from each other and the sheet of material 115 may beinserted or placed on the leading edges 122 of the creasing elements 14of the bottom array 12, and subsequently the first or top array 10 maybe actuated downwardly to cause the leading edges 120 of the creasingelements 13 of the first or top array 10 to contact surface of the sheetof material 115 (see FIGS. 17, 19, and 20).

As the folding operation proceeds, the top array 10 is actuated furtherdownwardly along the z direction, for example by actuation assembly 25,moving the leading edges 120 of the creasing elements 13 of the toparray 10 below the plane defined by the leading edges 122 of thecreasing elements 14 of the bottom array 12. In this manner, the firstarray 10 and second array 12 of creasing elements 13, 14 are moved to asecond position relative to each other where the creasing elements 13 ofthe first array 10 are at least partially interdigitated with thecreasing elements 14 of the second array 12 (see FIGS. 21, 23, and 24).

During downward motion of the top array 10 to its second or partiallyinterdigitated position, individual creasing elements 13 of the toparray 10 may be brought closer together along the x direction, forexample by use of first and second top x actuators 18 a, 18 c and firstand second top x rack and pinion assemblies 42 a, 42 c, therebycollapsing the top array 10 along the x direction. In this regard,actuators 18 a, 18 c can serve to rotate the gearing mechanisms or rackand pinion assemblies 42 a, 42 c to decrease the distance between top xpush/pull bars 51, 52 thereby contracting the top array 10 in the xdirection. In a similar manner, individual creasing elements 14 of thebottom array 12 may be brought closer together along the x direction,for example by use of bottom x actuators 20 a, 20 c and first and secondbottom x rack and pinion assemblies 45 a, 45 c, thereby collapsing thebottom array 12 along the x direction. In this regard, actuators 20 a,20 c can serve to rotate the gearing mechanisms or rack and pinionassemblies 45 a, 45 c to decrease the distance between bottom xpush/pull bars 51, 52 thereby contracting the bottom array 10 in the xdirection.

The x push/pull bars 51, 52, which may be rigidly or otherwise coupledto the sides of the arrays 10, 12, for example using the y-guides 57,58, may be translated along the x direction to cause the collapsing andcontracting of the arrays 10, 12. An inward or compressive force is thusapplied by one or more of the x push/pull bars 51, 52 to the sides ofthe arrays 10, 12 which span the y direction. The force is generallyapplied to the end row of creasing elements and transmitted, for examplevia rigid body motion of the end row of creasing elements, to each ofthe end x-travel scissor assemblies 152 and thus to each other creasingelement in such row. The rigid body motion of each of the end creasingelements may force the unconstrained portion of the scissor assemblies152, for example the pivotally mounted ends 166, to translate within theslots 168 moving the pivotally mounted ends 166 downward, in the case ofthe bottom set of x-travel scissor assemblies, and upward, in the caseof the top set of x-travel scissor assemblies (see FIG. 19). Thepivotally mounted ends 166 are coupled to adjacent ones of the pivotallymounted ends 166 and as such they move in unison under the compressiveforce of the x push/pull bars 51, 52. Since the creasing elements ineach row are coupled by the y-travel scissor assemblies 154 to adjacentcreasing elements in the next or adjacent row, movement of certain rowsof creasing elements by the x push/pull bars 51, 52 cause similarmovement in the x direction of all of the creasing elements in thearray.

In an analogous manner, a compressive or inward force may be exerted bythe y push/pull bars 53, 54 which is applied to the end columns andcertain of the internal or central columns of creasing elements via thex-guides 55, 56 mounted to such bars 53, 54 and connected to suchcolumns of creasing elements. The inward motion of such columns ofcreasing elements of the top and bottom arrays 10, 12 causes they-travel scissor assemblies 154 of such columns to fold or collapse andthe pivotally mounted ends 162 to move within slot 165 in a downwarddirection, in the case of the bottom array 12, or an upward direction,in the case of the top array 10. Pins 163 couple each of the pivotallymounted ends 162 to each other causing them to slide up and down inunison. Since the creasing elements in each column are coupled by thex-travel scissor assemblies 152 to adjacent creasing elements in thenext or adjacent column, movement of certain columns of creasingelements by the y push/pull bars 53, 54 cause similar movement in the ydirection of all of the creasing elements in the array.

In one embodiment, the contraction of the top array 10 and top array 12are coordinated and thus occur simultaneously such that the top array 10and bottom array 12 contract in unison in the x direction. The downwardmotion along the z direction and contracting motion along the xdirection of the arrays 10, 12 may be coordinated such that the relativedistance 185 between the leading edges 120 of the creasing elements 13of the top array 10 and the leading edges 122 of the creasing elements14 of the bottom array 12 remains generally constant (see FIG. 19). Inthis manner, tearing or other damage to the sheet of material 115 may beprevented. In some examples, the coordination of relative movement ofthe arrays 10, 12 may be adjusted such that the relative distance 185 isallowed to vary thereby imparting a stretching force to the sheet ofmaterial 115, which sheet in some examples may be made of a compliantmaterial. For example, and with reference to FIG. 19, the leading edges122 of bottom creasing elements 14 contact the sheet of material 115along a first plurality of straight line segments 87 along the y axis.The leading edges 120 of top creasing elements 13 contact the sheet ofmaterial 115 along a second plurality of straight line segments 87 alongthe y axis. In one embodiment, the straight line segment 87 contacted orengaged by a creasing element 13 in a row of top array 10 is adjacentthe straight line segment 87 contacted or engaged by the adjacentcreasing element 14 of the bottom array 12 in a corresponding row. Theportion of the material 115 which includes the chevron or angled legs83, 85 of the crease paths is not engaged by any surface or edge of thecreasing elements at this stage. That portion remains unsupported by thecreasing elements and disposed between adjacent columns of creasingelements. As the top and bottom arrays 10, 12 become partiallyinterdigitated, the first plurality of straight line segments engaged bythe top array 10 moves downwardly, while the second plurality ofstraight line segments engaged by the bottom 12 moves upwardly to formthe accordion-like pattern of troughs or valleys 86 and peaks or folds80 described previously with reference to FIGS. 5-10. The materialspanning the chevrons or angled legs 83, 85 also folds in a similarmanner by virtue of being connected to the straight line segments 87,which are in engagement with the plurality of creasing elements 13, 14.The folding of the unsupported material causes first spaced apartendwalls 72 and second spaced apart endwalls 74 to begin taking shape bybringing the two plies of each wall closer together.

In a next stage of the folding operation, the top array 10 and bottomarray 12 of creasing elements 13, 14 are contracted in the y direction,which as described above may be accomplished by bringing the y-push/pullbars 53, 54 closer together. During this stage, the material extendingunsupported between the columns of creasing elements, for example theportion of the medium 60 spanning the chevrons or angled legs 83, 85that is to become the spaced apart endwalls 72, 74, may be forced tofold in a forward or a backward direction, as may be desired. Aspreviously described, selectively perforating or scoring the medium 60or 115 along only one side of the medium may dictate the direction ofthe fold. By providing certain crease paths, for example the creasepaths 75, only along one face of the foldable medium 60 or 115, thefacets 102, 103 (see FIG. 9) defined by the chevrons or angled legs 83,85 may be forced to fold in a forward direction relative to the faces101, as shown for example in FIG. 21. Each endwall 72 may be formed apair of adjacent facets 102 and each endwall 74 may be formed from thepair of adjacent facets 103, each with respect to the x axis and asshown for example in FIG. 9. In this step, and as the columns ofcreasing elements move closer together, adjacent pairs of endwalls 72,74 are further collapsed to form the four ply wall structures 82.

The top array 10 and bottom array 12 may move through severalintermediate positions of interdigitations during the folding operation.Furthermore, in certain embodiments, contraction of the arrays 10, 12 inthe y direction may occur simultaneously with or separately fromcontraction of the arrays 10, 12 along the x direction, and contractionor interdigitation of the arrays 10, 12 in the z direction 15 may occursimultaneously with or separately from contraction of the arrays in oneor both of the x and y directions. For example, the arrays may be movedfrom the noninterdigitated position, for example where the top array 10and bottom array 12 are farthest apart, to the fully interdigitatedposition, for example where the creasing elements 13, 14 are closesttogether along the x direction, before or while contracting of thearrays occurs along the y direction.

As the arrays 10, 12 move from a partially interdigitated or secondposition to a fully interdigitated or third position, the x-travelscissor assemblies may become fully collapsed, and as the arrays 10 and12 are fully contracted along the y direction, the y-travel scissorassemblies may also become fully collapsed to form the compactconfiguration shown in FIGS. 25-30. At this point, the medium 60 or 115is folded to its final folded configuration, for example as depicted inFIG. 31 and as also depicted and described in reference to FIGS. 7 and8. In this fully collapsed position, each two abutting endwalls 72, 74may become sandwiched or compressed by the sides 128, 130 of the topportion of adjacent creasing elements, particularly for example wherethe length of the leading edges 120, 122 of the elements issubstantially equal to the straight line segments 87 of the medium, andboth sides of each of the adjacent sloped sidewalls or facets 76 78 of acell 63 may come in full contact with the sloping sides faces 124, 126of the respective creasing element. In other words, the interdigitationof the top portions 150 of the creasing elements 13, 14 and thecontraction along the y axis of the arrays 10, 12 of creasing elementsoperates to fold the medium 60 or 115 into a three-dimensional structure61, for example as shown in FIGS. 7-8 and 31.

After the three-dimensional structure 61 has been formed, one or both ofthe arrays 10, 12 may be actuated along the z axis or direction 15 awayfrom each other to allow for the formed structure to be retrieved fromthe apparatus 1. For example, the top array 10 may be actuated using thelinear actuator 8 along the z axis or vertical direction 15. The foldedthree-dimensional structure 61 may be removed from the bottom array 12and may then be available for use or further processing. Each of the toparray 10 and bottom array 12 may then be expanded to their respectivefirst, starting or home position, with the expansion of each of the topand bottom arrays 10, 12 occurring simultaneously or in sequence. Forexample, array 10 may be expanded along the x direction by moving thex-push/pull bars 51, 52 from the contracted position shown in FIG. 25 tothe farthest apart position shown in FIGS. 4 and 12 by rotating thepinion gears 17, 34 of the rack and pinion assemblies 45 a, 45 c in aclockwise direction. The pairs of rack gears 19, 21 and 39, 41 maytranslate along the x direction ends of the outer ends of the rack gearsmoving farther apart and thereby causing the x-push/pull bars to movefarther apart. As previously described, each of the x-push/pull bars maybe coupled, rigidly or otherwise, to the end rows of the arrays 10, 12,and the outward movement of the x-push/pull bars causes the end row ofcreasing elements to move outwardly. As during the contraction of thearray, by virtue of interconnecting each creasing element or foldingelement to the next or adjacent creasing element or folding elementusing x-travel scissor assemblies 152, the pulling motion or forceapplied to the end rows of the creasing elements is transmitted towardsthe interior of the array causing all interior x-travel scissorassemblies 152 to expand.

The array 10 may be expanded along the y direction in an analogousmanner by moving the y-push/pull bars 53, 54 from the contractedposition of FIG. 25 to the expanded or home position of FIGS. 4 and 12.Rotation of the pinion gears 27 and 47 in the clockwise direction causesthe pairs of rack gears 46, 48 and 26, 28 to move along the y directionsuch that outer ends of the rack gears move apart from each otherthereby causing the y-push/pull bars 53, 54, which are coupled to theends of the racks, to move outwardly relative to each other. Theexpansion of the y-push/pull bars 53, 54 applies a pulling force alongthe top and bottom end columns of creasing elements, for example bymeans of x-guides 55, 56. The pulling force along the end columns istransmitted to the interior of the array causing all of the y-travelscissor assemblies 154 to expand.

In the present example, four x-guides 55 are used at the front side ofthe arrays and four x-guides 56 are used at the back or rear side of thearrays, however any other number of x-guides may be used. Similarly, twoy-guides 57 and two y-guides 58 are used to couple the left and rightsides of each array to the respective push/pull bars of the portion ofapparatus 1, however any other number, for example four, eight or more,of guides may be used along each side. As will be appreciated, thex-travel scissor assemblies 152 allow the arrays 10, 12 to collapse orcontract or expand when an appropriate force is applied along the xdirection. When a force is instead applied along the y direction, thex-travel scissor elements act as a generally rigid link connecting eachof the creasing elements of a column of creasing elements forming agenerally rigid column or beam. Similarly, the y-travel scissorassemblies 154 allow contraction or expansion along the y direction butform a generally rigid coupling along rows of creasing elements. In thismanner, a pulling force applied perpendicular at one or more pointsalong the generally rigid column of creasing elements may be sufficientto cause all of the creasing elements in the column to move in reactionto that force. Similarly, a pulling force applied perpendicular to therigid row assemblies formed by interconnected creasing elements andy-travel scissor assemblies may be sufficient to cause the rows ofelements to move along the pulling force. In this regard, thecombination of orthogonally arranged x-travel and y-travel scissorassemblies 152, 154 not only allows for collapsing of the arrays butalso advantageously forms generally rigid rows and columns of creasingelements allowing for the expansion of the arrays.

In one embodiment, the angle by the inclined faces 124, 126 forming theleading edge 120, 122 of a creasing element is not greater than, orsubstantially equal to or less than, the angle between the sloped sidewalls or facets 76, 78 of the desired cell 63 to be formed by thecreasing element. In one embodiment, apparatus 1 is constructed so thatthe angle between the inclined faces 124, 126 of the creasing elements13, 14 is less than or equal to the smallest desired angle between thesloped side walls or facets 76, 78 of the cells 63 in the foldedstructure 61 intended to be created by such creasing elements 13, 14.

The depth of the cells 63 in the folded structure 61 created byapparatus is determined by the amount of full interdigitation of thecreasing elements 13, 14 forming such cells 63, that is the distancealong the z axis that the leading edge 120 of the respective creasingelements 13 extend between and beyond the leading edge 122 of therespective creasing elements 14 forming the cell. In one embodiment, theamount or distance of full interdigitation between a creasing element 13of top array 10 and adjacent creasing elements 14 of bottom array 12permitted by apparatus 1 is not less than the maximum distance along thez axis that valley fold 86 of the desired cell 63 to be created extendsbelow the opposed end walls 72, 74 of such cell 63.

Each cell 63 of the folded structure 61 has a width along the x axis anda length along the y axis. The width of a cell 63, which is generallythe distance between adjacent peak folds 80 is determined by the amountor distance along the x axis to which the leading edges 120, 122 ofadjacent creasing elements of the first and second arrays 10, 12contract to in the final or contracted position. The length of a cell63, which is generally the length of the straight line segment 87, isdefined by the cumulative length of opposing leading edges 120, 122 ofopposing creasing elements. That is, in some examples, the top andbottom arrays may be offset along the y direction to vary the length ofeach resulting cell. The configuration and operation of an apparatusaccording to the present invention to achieve offsetting of the arraysalong the y direction, for example, will be further described withreference to FIGS. 32 and 33 below.

Further variations of the resulting cells 63 may be achieved. Forexample, if the leading edge 122 of the opposed creasing element in thesecond array of the apparatus 1 forming such cell is located betweensuch creasing elements of the first array an equal distance from eachsuch creasing element of the first array, then valley fold 86 of thecell will be located in the middle of the cell. Alternatively, if theleading edge 122 of the opposed creasing element of the second array isspaced closer to the leading edge 122 of one of the adjacent creasingelements of the first array, then the valley fold 86 of the cell willlikewise be closer to one of the peak folds 80 of the cell. In oneembodiment, the amount or distance along the x axis of the leading edge122 of adjacent creasing elements of the first array 10, 12 permitted byapparatus 1 is not less than the maximum distance along the x axis thatof the peak folds 80 of the desired cell 63 to be created by theapparatus.

As can be appreciated from the foregoing, apparatus 1 permits foldedstructures 61 to be created having cells 63 therein of various shapesand sizes.

As previously discussed, an apparatus of the invention call also beprovided that permits the length of a cell 63 of the formed foldedstructure 61 to be varied from structure to structure, which may beachieved without changing the size of the creasing elements or otherwisereconfiguring the top and/or bottom arrays 10,12. As such, opposedcreasing elements having respective leading edges 120, 122 of fixedlengths can be utilized with a foldable medium 60 having an imaginarystraight line segment 87 of a first length defined thereon, so as toform a first cell 63 having a distance or length between opposed endwalls 72, 74 of such first length. In addition, such opposed creasingelements can be utilized with a foldable medium 60 having anotherimaginary straight line segment 87 of a second length defined thereon,that is different from the first length, such that a second cell 63having a distance between opposed end walls 72, 74 of such second lengthmay be formed. One embodiment of such an apparatus is illustrated inFIG. 32, which for simplicity and clarity shows a partial isometric viewof the apparatus. In the example shown in FIG. 32, certain components ofthe actuating assemblies and support assemblies are shown, while certainother portions of the apparatus, for example the top and bottom arrays10,12, are omitted so as not to obscure the disclosure of the presentexample. The arrays 10,12 (not shown in FIG. 32) may be essentially thesame as previously described with reference to apparatus 1, and it willbe understood that any combinations of creasing elements and arrays ofcreasing elements may be used in the example of FIG. 32.

Apparatus 201 illustrated in FIG. 32 is substantially similar toapparatus 1 and like reference numerals have been utilized to describeand identify like components of apparatus 1 and 201. Apparatus 201permits relative movement along at least one of x and y axes between thecreasing elements 13 of top array 10 and the creasing elements 14 of thebottom array 12 (not shown in FIG. 32). In one embodiment, creasingelements 13 of the top array are movable in unison in a direction alongthe y axis relative to the creasing elements 14 of the bottom array.Although such movement can be of any suitable distance, in oneembodiment such distance ranges from 0.125 to 1.0 inch, in oneembodiment from 0.125 to 0.5 inch and in one embodiment is approximately0.25 inch.

In one embodiment, an additional moveable plate 202 is included inapparatus 201. Translation plate 202, also known as y-translation plate202, is slidably secured to the bottom of moveable plate 6 by anysuitable slide assembly 203. In one embodiment, the slide assemblyincludes at least first and second grooves 206 a, 206 b formed in thebottom of plate 6 in spaced-apart positions along the x axis.Translation plate 202 is provided with at least first and second slideelements 207 a, 207 b for cooperating with respective grooves 206 topermit plate 208 to move in the y direction relative to plate 6. Theslide elements 207 can be in the form of first and second rails 207 a,207 b that cooperatively seat in respective grooves 206 a, 206 b in amanner with permits the rails to slide along the y axis or 215direction, in the grooves. The rails 207 a, 207 b and grooves 206 a, 206b can be configured such that the rails are restricted from moving inthe two directions orthogonal to the direction of travel, and as suchthe rails 207 a, 207 b and grooves 206 a, 206 b may be shaped so thatthe rails 207 a, 207 b cannot move in the x direction or in the zdirection while seated in the grooves 206 a, 206 b. The cooperatingrails and grooves may be implemented in a dovetail arrangement, as shownin FIG. 32, however other techniques, currently known or laterdeveloped, for slidably coupling the plate 202 to the bottom of plate 6may be used.

Rack and pinion assemblies 42 can be mounted to the bottom 213 oftranslation plate 202 in the same configuration as such assemblies 42are mounted to the bottom of moveable plate 6 in apparatus 1. Similarly,actuation devices or actuators 18 a-18 d are mounted to the top ofmovable plate 6, and rack and pinions assemblies 42, in the same manneras discussed above and illustrated with respect to moveable plate 6 inapparatus 1. A plurality of respective apertures 211 can be providedthrough the width of translation plate 202 for receiving the actuators18 and permitting movement of the actuators 18 along the y axis during ytravel of the plate 202. In some examples, the apertures 211 may becircular and a diameter of each of the apertures 211 may be selectedsuch that the inner wall of the aperture 211 does not interfere with theshaft of each of the actuators 18 a-18 d when the plate 203 istranslated along the y direction. In certain examples, one or more ofthe apertures 211 may shaped as an oval, a rectangle, or an elongatedslot. Any other suitable form factor may be used for the apertures 211to allow the plate 202 to move relative the plates 2, 4, and/or 6 alongthe y direction.

An actuation assembly 216 can be included in apparatus 201 fortranslating or moving plate 202 relative to elevationally-adjustableplate 6. In one embodiment, a plurality of linear actuators 217, forexample cylinder-piston type, hydraulic or electric actuators, may beutilized and controlled and/or synchronized as desired, using aprogrammable controller for example that is the same or in addition tothe controllers discussed above. In one embodiment, first and secondactuators 217 are provided and mounted in spaced-apart positions alongthe x axis to the top of moveable plate 6. The piston of each actuatorcan be connected to a bracket or other suitable member 218 that isjoined in a suitable manner to the top of translation plate 202 andextends through an opening in the moveable plate 6 so as to beaccessible to the actuator.

Actuation assembly 216 permits the creasing elements 13 of top array 10to be moveable along y axis relative to the creasing elements 14 of thebottom array 12 (see FIG. 33). As such, the rows 33 of creasing elements13 can be translated in the y direction relative to the correspondingrows 34 of creasing elements 14, either during or prior to the foldingprocess of apparatus 201.

Apparatus 201 operates in substantially the same manner as discussedabove with respect to apparatus 1. In one method of operation where thestraight lines 87 of the foldable medium 60, and thus the distancebetween end walls 72, 74 of the cells 63 of the folded structure to beformed, are greater than the length of the leading edge of the creasingelement 13, 14, the top array 10 can be moved along the y axis relativeto the bottom array 12, for example before the creasing elements engagethe foldable medium 60, such that the end surface of the creasingelements in one of arrays 10, 12 is registered along the y axis with oneend of an alternating set of straight lines 87 of the medium 60 and theend surface of the creasing elements in the other of arrays 10, 12 isregistered along the y axis with the other end of each of the set ofstraight lines 87 between such alternating set. For example, the endsurface 130 of a creasing element 13 can be registered with one end of astraight line 87 of the medium 60, and the end surfaces 130 of theopposing creasing elements 14 on both sides along the x axis of suchcreasing element 13 can be registered with the other end of the twoadjacent straight lines 87 on the medium located on opposite sides ofthe first line 87 along the x axis. During the folding process, theopposed leading edges 120, 122 of the creasing elements 13, 14 engagethe straight lines 87 of the medium 60 during interdigitation of thecreasing elements to cause such alternating straight lines 87 to formalternating peak folds 80 and valley folds 86 in the medium. A slightoffset of the top creasing elements 13 relative to the bottom creasingelements 14 along the y axis as shown in FIG. 33, such as for example inthe amounts discussed above, does not affect the folding process or theformation of cells 63 and wall structures 82.

In the foregoing manner, apparatus 201 permits creasing elements 13, 14having leading edges 120, 122 of fixed lengths to be utilized to formcells having a distance between end walls 72, 74 approximately equal tothe length of such leading edges 120, 122 and to form cells having adistance between end walls 72, 74 greater than the length of suchleading edges 120, 122.

Other embodiments of the first or top array of creasing elements and thesecond or bottom array of creasing elements of the creasing assembly ofthe present invention, for example creasing assembly 7, can be provided.An additional embodiment of an array of creasing elements that can beutilized for one or both of top array 10 and bottom array 12 of theinvention is illustrated in FIGS. 34-36. Creasing array 301 disclosed inFIGS. 34-36 can be utilized for one or both of top array 10 and bottomarray 12 of the invention, including in any of the disclosures above orherein. The creasing array 301 is substantially similar to top array 10and bottom array 12 and like reference numerals have been used todescribe like components of arrays 301, 10 and 12.

Creasing array 301 is formed from a plurality of creasing elements 302that are substantially similar to creasing elements 13 of top array 10and creasing elements 14 of bottom array 12 and like reference numeralshave been used to describe like components of creasing elements 302, 13and 14. The creasing elements can be arranged in a plurality of columns303 and a plurality of rows 304 that can extend perpendicular to thecolumns 303. It is appreciated that some or all of creasing elements 302of creasing array 301 can be substantially identical and, in oneembodiment, for example as illustrated in FIGS. 34-36, all of creasingelements 302 are identical. Each individual creasing element 302, whichmay also be referred to as a creasing member or a folding element ormember, may be implemented as a generally elongate member, which mayhave a rectangular transverse cross section. It is appreciated that someor all of the creasing elements may be configured to have substantiallyany transverse cross section, for example such creasing elements may becircular or oval in the transverse cross-section such that the creasingelements are generally shaped as rods or other cylindrical members.Other form factors may be used as desired for forming some or all of thecreasing elements.

In one embodiment, each creasing element 302 includes a first or topportion 150 and a second or body portion 306 (see FIG. 34). Body portion306 of a creasing element can include a top, distal or upper section 307and a bottom, proximal or lower section 308, as shown in FIG. 34. Thebody portion 306 of each creasing element 302 may be shaped andconfigured in any manner desired which accommodates coupling the bodyportion 306 of each creasing element of the array 301 and which furtheraccommodates coupling the array to the actuation assembly 5. In oneembodiment, as discussed above, the creasing elements of each array arearranged in rows and columns such that each creasing element is adjacentto at least one and preferably a plurality of other creasing elements.For example as shown in FIG. 34, creasing element 302 e is adjacent toand disposed between creasing elements 302 d, 302 f along the xdirection and adjacent to and disposed between creasing elements 302 b,302 h in the y direction.

Adjacent creasing elements can be connected together using any suitablelinking assemblies, including any of the linking assemblies describedherein, which can permit expansion and contraction of columns ofcreasing elements along the y axis and expansion and contraction of rowsof creasing elements along the x axis. In one embodiment, the expansionand contraction of the creasing elements in the y axis is independent ofthe expansion and contraction of the creasing elements in the x axis.The linking assemblies may be configured such that all creasing elementsin a row 304 of creasing elements are moveable together in a firstdirection, for example along the y axis, and all creasing elements in acolumn 303 of creasing elements are moveable together in a seconddirection, for example along the x axis. In one embodiment, the linkingassemblies, which may interchangeably be referred to herein asexpandable linking assemblies or directionally expandable linkingassemblies, may be implemented using y-travel scissor assemblies 316 andx-travel scissor assemblies 317 for respectively coupling togethercolumns 303 of creasing elements 302 and rows 304 of creasing elements302.

Each y-travel 316 and x-travel 317 scissor assembly, which can be madefrom any suitable material such as metal or plastic or ceramic, caninclude a plurality of first and second scissor elements or links. Forexample, each y-travel scissor assembly 316 may include a plurality offirst y-scissor links 321 and a plurality of second y-scissor links 322(see FIG. 34). The first and second y-scissor links 321, 322 arepivotaly coupled together using a pivot means or joint that can includefor example a y-center pivot element or pin 323. Each y-scissor link321, 322 has a y-first end portion 326 and a y-second end 327. In oneembodiment, each pair of y-scissor links 321, 322 couples together threeadjacent creasing elements in a column 303 at the upper section 307 ofthe creasing elements 302. In this regard, the y-first end 326 of eachy-scissor link 321, 322 may be slidably coupled to upper section 307 ofthe body portion 306 of one of the outer creasing elements of such threeadjacent creasing elements, for example the left creasing element 302,by for example using a y-moveable element or pin 328 slidably disposedin a respective y-slot 331, 332 provided on the upper section 307 ofsuch left creasing element 302 and extending longitudinally in the zdirection. The y-slot 331 for the y-first end 326 of the first y-scissorlink 321 can be in the lower portion of the upper section 307, and they-slot 332 for the y-first end 326 of the second y-scissor link 322 canbe in the upper portion of the upper section 307. The y-second end 327of each y-scissor link 321, 322 may be slidably coupled to upper section307 of the body portion 306 of the other of the outer creasing elementsof such three adjacent creasing elements, for example the right creasingelement 302, by for example using a y-moveable element or pin 328slidably disposed in a respective y-slot 332,331 provided on the uppersection 307 of such right creasing element 302 and extendinglongitudinally in the z direction. The y-slot 332 for the y-second end327 of the first y-scissor link 321 can be in the upper portion of theupper section 307, and the y-slot 331 for the y-second end 327 of thesecond y-scissor link 322 can be in the lower portion of the uppersection 307. The y-center pivot pin 323 is fixedly coupled within a bore(not shown) in the upper section 307 of the center creasing element 302of such three adjacent creasing elements. In one embodiment, such borein the creasing element 302 is disposed midway between the slots 331,332. In one embodiment, a first y-travel scissor assembly 316 is coupledto one side of the creasing elements 302 of each column 303 of creasingelements and a second y-travel scissor assembly 316 is coupled to theother side of the creasing elements 302 of such column 303, although itis appreciated that an embodiment can be provided where only oney-travel scissor assembly 316 is utilized for a column 303 of creasingelements 302. At the outer-most rows 304 of creasing elements 302, onlyhalf of each y-scissor link 321, 322 is fixedly coupled by the y-centerpivot pin 323 to the upper section 307 of each such end creasing element302. In this regard, a y-end portion 326 or 327 of each scissor link321, 322 extends from the end creasing element 302 to the respectiveslot 331, 332 in the adjacent creasing element 302 disposed inwardly ofthe array 301 from such end creasing element. Each first y-scissor link321 extends parallel to each other and each second y-scissor link 322extends parallel to each to each and the y-travel scissor assembly 316extends in a plane. Contraction of the scissor links 321,322 of theassembly 316, by pivoting y-first end portions 326 away from each otherabout pin 323 and y-second end portions 327 away from each other aboutpin 323, causes the y-moveable pins 328 of each creasing element 302 tomove away from each other in slots 331, 332 so as to draw the creasingelements of the array 301 together in the y direction in unison.Expansion of the links 321, 322 of the assembly 316, by pivoting y-firstend portions 326 towards each other about pin 323 and y-second endportions 327 towards each other about pin 323, causes the y-moveablepins 328 of each creasing element 302 to move towards each other inslots 331, 332 so as to move the creasing elements of the array 301 awayfrom each other or expand in the y direction in unison.

In a similar manner, each x-travel scissor assembly 317 may include aplurality of first x-scissor links 341 and a plurality of secondx-scissor links 342 (see FIG. 36). The first and second x-scissor links341, 342 are pivotaly coupled together using a pivot means or joint thatcan include for example a x-center pivot element or pin 343. Eachx-scissor link 341, 342 has an x-first end portion 346 and a x-secondend 347. In one embodiment, each pair of x-scissor links 341, 342couples together three adjacent creasing elements in a row 304 at thelower section 308 of the creasing elements 302. In this regard, thex-first end 346 of each x-scissor link 341, 342 may be slidably coupledto lower section 308 of the body portion 306 of one of the outercreasing elements of such three adjacent creasing elements, for examplethe left creasing element 302, by for example using a x-moveable elementor pin 348 slidably disposed in a respective x-slot 351, 352 provided onthe lower section 308 of such left creasing element 302 and extendinglongitudinally in the z direction. The x-slot 351 for the x-first end346 of the first x-scissor link 341 can be in the lower portion of thelower section 308, and the x-slot 352 for the x-first end 346 of thesecond x-scissor link 342 can be in the upper portion of the lowersection 308. The x-second end 347 of each x-scissor link 341, 342 may beslidably coupled to lower section 308 of the body portion 306 of theother of the outer creasing elements of such three adjacent creasingelements, for example the right creasing element 302, by for exampleusing a x-moveable element or pin 348 slidably disposed in a respectivex-slot 352, 351 provided on the lower section 308 of such right creasingelement 302 and extending longitudinally in the z direction. The x-slot352 for the x-second end 347 of the first x-scissor link 341 can be inthe upper portion of the lower section 308, and the x-slot 351 for thex-second end 347 of the second x-scissor link 342 can be in the lowerportion of the lower section 308. The x-center pivot pin 343 is fixedlycoupled within a bore (not shown) in the lower section 308 of the centercreasing element 302 of such three adjacent creasing elements. In oneembodiment, such bore in the creasing element 302 is disposed midwaybetween the slots 351, 352. In one embodiment, a first x-travel scissorassembly 316 is coupled to one side of the creasing elements 302 of eachrow 304 of creasing elements and a second x-travel scissor assembly 316is coupled to the other side of the creasing elements 302 of such row304, although it is appreciated that an embodiment can be provided whereonly one x-travel scissor assembly 316 is utilized for a row 304 ofcreasing elements 302. At the outer-most columns 303 of creasingelements 302, only half of each x-scissor link 341, 342 is fixedlycoupled by the x-center pivot pin 343 to the lower section 308 of eachsuch end creasing element 302. In this regard, a x-end portion 346 or347 of each scissor link 341, 342 extends from the end creasing element302 to the respective slot 351, 352 in the adjacent creasing element 302disposed inwardly of the array 301 from such end creasing element. Eachfirst x-scissor link 341 extends parallel to each other and each secondx-scissor link 342 extends parallel to each to each and the x-travelscissor assembly 316 extends in a plane. Contraction of the scissorlinks 341, 342 of the assembly 316, by pivoting x-first end portions 346away from each other about pin 343 and x-second end portions 347 awayfrom each other about pin 343, causes the x-moveable pins 348 of eachcreasing element 302 to move away from each other in slots 351, 352 soas to draw the creasing elements of the array 301 together in the xdirection in unison. Expansion of the links 341, 342 of the assembly316, by pivoting x-first end portions 346 towards each other about pin343 and x-second end portions 347 towards each other about pin 343,causes the x-moveable pins 348 of each creasing element 302 to movetowards each other in slots 351, 352 so as to move the creasing elementsof the array 301 away from each other or expand in the x direction inunison.

The creasing elements 302 can be made from any suitable material such asmetal, plastic or a ceramic material, and in one embodiment can be madefrom a rigid such material. Not all of the creasing elements need bemade from the same material, for example some creasing elements can bemade from a rigid plastic, some other creasing elements can be made frommetal and some other creasing elements can be made from a ceramicmaterial. In one embodiment, the top 150 and body 306 portions of eachcreasing element 302 may be formed as a single unitary structure, forexample a monolithic component fabricated in one piece by molding ormachining, as examples. In one embodiment, each creasing element maycomprise a plurality of individual sub-components which are assembled toform the creasing element and assembled into the array 301 of creasingelements. In one embodiment, an end portion 173 of the lower section 308of a creasing element 302 may be provided with a sliding contact surfaceor bearing 175.

Creasing array 301 can operate in the same manner as discussed above,for example with respect to top array 10 and bottom array 12. Thespanning of the first and second y-scissor links 321, 322 and the firstand second x-scissor links 341, 342 across three respective adjacentcreasing elements 302, and the slidable coupling together of such threeadjacent creasing elements 302 by such respective scissor links,enhances the structural integrity and uniform movement of the creasingarray 301 so as to increase the reliability of the operation of foldingapparatus 1 and the quality of the folded structure formed thereby.

Examples of apparatus, systems and methods for folding a sheet ofmaterial into a folded support structure have been described herein,which apparatus, systems, and methods may afford a level of automationfor achieving three dimensional folded structures as described.

An exemplary apparatus according to the present invention may include afirst array of creasing elements and a second array of creasingelements, each of the creasing elements in the first and second arrayshaving a leading edge adapted to engage a sheet of material. Theapparatus may further include at least one actuator for causing relativemovement of the first and second arrays of creasing elements from afirst position in which the first and second plurality of creasingelements are spaced apart to a second position in which the first andsecond array of creasing elements are at least partially interdigitatedand for moving the creasing elements of the first array closer togetherand the creasing elements of the second array closer together duringrelative movement of the first and second arrays of creasing elements tothe second position. In this manner a sheet of material can be placedbetween the first and second arrays of creasing elements and folded bythe leading edges of the creasing elements during the relative movementof the first and second arrays creasing elements to the second position.Furthermore, the movement of the creasing elements of the first arraycloser together and the creasing elements of the second array closertogether accommodates contraction of the sheet of material as it isfolded by the first and second arrays of creasing elements.

In certain embodiments, the at least on actuator may include at leastone first actuator for causing relative movement of the first and secondarrays of creasing elements from the first position to the secondposition and at least one second actuator for moving the creasingelements of the first array closer together and the creasing elements ofthe second array closer together during relative movement of the firstand second arrays of creasing elements to the second position. In oneembodiment, an apparatus may include a plurality of arrays of creasingelements, wherein creasing elements of a first array are disposed inrows and columns and the creasing elements of a second array aredisposed in rows and columns. In one embodiment, the number of columnsin the first array of creasing elements may be one less than the numberof columns in the second array of creasing elements. In one embodiment,the rows of creasing elements in the first array may be alignable in aplane with the rows of creasing elements in the second array.

In one embodiment, the first array of creasing elements may be moveabletransversely relative to the second array of creasing elements so thatthe rows of creasing elements in the first array are not aligned in aplane with the rows of creasing elements in the second array. In oneembodiment, the apparatus may further include at least one additionalactuator for moving the first array of creasing elements relative to thesecond array of creasing elements so that the rows of creasing elementsin the first array are not aligned in a plane with the rows of creasingelements in the second array when the first and second arrays ofcreasing elements are in the first position.

In one embodiment, the columns of creasing elements in the first arraymay be offset from the columns of creasing elements in the second arraywhen viewed in plan so that that columns of creasing elements in thefirst array are interdigitated with the columns of creasing elements inthe second array when the first and second arrays of creasing elementsare in the second position. In one embodiment, the columns of creasingelements in the first array may be substantially centered between thecolumns of creasing elements in the second array when viewed in plan.

In one embodiment, adjacent creasing elements in each column of thefirst array may be interconnected by a first column scissor assembly andadjacent creasing elements in each column of the second array may beinterconnected by a second column scissor assembly. In one embodiment,adjacent creasing elements in each row of the first array may beinterconnected by a first row scissor assembly and adjacent creasingelements in each row of the second array may be interconnected by asecond row scissor assembly.

In one embodiment, leading edges of the creasing elements of the firstarray may be substantially coplanar with each other when the first andsecond arrays of creasing elements are in the first position. In oneembodiment, the leading edges of the creasing elements of the secondarray may be substantially coplanar with each other when the first andsecond arrays of creasing elements are in the first position. In oneembodiment, the leading edge of the creasing elements of the secondarray may be substantially coplanar with each other and the leading edgeof the creasing elements of the first array may be substantiallycoplanar with each other when the first and second arrays of creasingelements are in the first position.

While various aspects and examples have been disclosed herein, otheraspects and examples will be apparent to those skilled in the art. Thevarious aspects and examples disclosed herein are for purposes ofillustration and are not intended to be limiting, with the true scopeand spirit being indicated by the following claims.

1. An apparatus for folding a sheet of material to create a foldedstructure, comprising a first array of creasing elements and a secondarray of creasing elements, each of the creasing elements having aleading edge adapted to engage the sheet of material, at least oneactuator for causing relative movement of the first and second arrays ofcreasing elements from a first position in which the first and secondplurality of creasing elements are spaced apart to a second position inwhich the first and second array of creasing elements are at leastpartially interdigitated and for moving the creasing elements of thefirst array closer together and the creasing elements of the secondarray closer together during relative movement of the first and secondarrays of creasing elements to the second position whereby the sheet ofmaterial can be placed between the first and second arrays of creasingelements and folded by the leading edges of the creasing elements duringthe relative movement of the first and second arrays creasing elementsto the second position and the movement of the creasing elements of thefirst array closer together and the creasing elements of the secondarray closer together accommodates contraction of the sheet of materialas it is folded by the first and second arrays of creasing elements. 2.The apparatus according to claim 1, wherein the at least on actuatorincludes at least one first actuator for causing relative movement ofthe first and second arrays of creasing elements from the first positionto the second position and at least one second actuator for moving thecreasing elements of the first array closer together and the creasingelements of the second array closer together during relative movement ofthe first and second arrays of creasing elements to the second position.3. The apparatus according to claim 1, wherein the creasing elements ofthe first array are disposed in rows and columns when viewed in plan andthe creasing elements of the second array are disposed in rows andcolumns when viewed in plan.
 4. The apparatus according to claim 3,wherein the number of columns in the first array of creasing elements isone less than the number of columns in the second array of creasingelements.
 5. The apparatus according to claim 4, wherein the number ofrows in the first array of creasing elements is equal to the number ofrows in the second array of creasing elements.
 6. The apparatusaccording to claim 3, wherein each of the rows of creasing elements inthe first array is alignable in a plane with the respective row ofcreasing elements in the second array.
 7. The apparatus according toclaim 6, wherein the first array of creasing elements are moveabletransversely relative to the second array of creasing elements so thatthe rows of creasing elements in the first array are not aligned in aplane with the rows of creasing elements in the second array.
 8. Theapparatus according to claim 7, further comprising at least oneadditional actuator for moving the first array of creasing elementsrelative to the second array of creasing elements so that the rows ofcreasing elements in the first array are not aligned in a plane with therows of creasing elements in the second array when the first and secondarrays of creasing elements are in the first position.
 9. The apparatusaccording to claim 3, wherein the columns of creasing elements in thefirst array are offset from the columns of creasing elements in thesecond array when viewed in plan so that that columns of creasingelements in the first array are interdigitated with the columns ofcreasing elements in the second array when the first and second arraysof creasing elements are in the second position.
 10. The apparatusaccording to claim 9, wherein the columns of creasing elements in thefirst array are substantially centered between the columns of creasingelements in the second array when viewed in plan.
 11. The apparatusaccording to claim 3, wherein adjacent creasing elements in each columnof the first array are interconnected by a first column scissor assemblyand adjacent creasing elements in each column of the second array areinterconnected by a second column scissor assembly.
 12. The apparatusaccording to claim 11, wherein adjacent creasing elements in each row ofthe first array are interconnected by a first row scissor assembly andadjacent creasing elements in each row of the second array areinterconnected by a second row scissor assembly.
 13. The apparatusaccording to claim 1, wherein the leading edges of the creasing elementsof the first array are substantially coplanar with each other when thefirst and second arrays of creasing elements are in the first position.14. The apparatus according to claim 13, wherein the leading edges ofthe creasing elements of the second array are substantially coplanarwith each other when the first and second arrays of creasing elementsare in the first position.
 15. The apparatus according to claim 14,wherein the leading edge of the creasing elements of the second arrayare substantially coplanar with each other and the leading edge of thecreasing elements of the first array are substantially coplanar witheach other when the first and second arrays of creasing elements are inthe first position.
 16. The apparatus according to claim 2, wherein theat least one actuator includes a third actuator for causing movement ofone of the first or second arrays relative to the other one of the firstor second arrays such that columns of creasing elements of one of thefirst or second arrays are not aligned with columns of creasing elementsof the other one of the first or second arrays.